Time Machine

Review this information carefully:

Types of disks you can use with Time Machine on Mac - Apple Support

You can use Time Machine with a network-attached storage (NAS) device that supports Time Machine over Server Message Block (SMB) or Apple Filing Protocol (AFP). It has been reported in these Discussions that some NAS that claim to support Time Machine actually do not work well with it.

The Time Machine backup needs to be APFS formatted (the only exception is for when you have been using a HFS+ disk with earlier MacOS and in those cases when you upgrade to Monterey or Ventura you may be able to continue with the HFS+ target for Time Machine).

The entire APFS volume is reserved for Time Machine backups. If you want to store files other than the Time Machine backup on the same physical device, use Disk Utility to create an additional APFS volume on the disk.

Transferring backups from one drive to another drive have proved to be difficult or impossible, given the postings on that topic in these Discussions. With APFS it is impossible for technical reasons, but even with HFS+ it has not succeeded consistently with recent versions of the MacOS.

The most straightforward options ahead for you would be:

• Use the NAS for misc. storage (if it is fast enough for you). If not, simply get a new external drive for misc storage. With a new external drive for misc storage, you can back it up along with your main drive to your Time Machine backup. You do this by removing the external drive from the Time Machine "exception" list in Time Machine Preference/Setting.
• If you use the NAS for misc storage, I'm not sure if it can be backed up (as a source drive) with Time Machine like an external drive can. Someone else who knows more about this might chime in here.
• Keep using your existing Time Machine drive for Time Machine. If it fills up obtain a new Time Machine drive and start a new set of backups on it, and keep the old one as an "Archive."

With Monterey and Ventura, I don't believe a NAS Time Machine drive can also be used for misc external storage if it is the Time Machine drive. Time Machine reserves the entire volume for Time Machine backups.

Message 01 or 02:

Whoever setup the Synology DS118 NAS drive for you & your daughter,

you should contact that person,

to arrange time to do config/settings changes,

& setup another SHARED FOLDER or another SHARED DRIVE/PARTITION inside the NAS drive,

with a new shared-name.

If you or your daughter, is able to able to do that, then you should do these steps together.

To use NAS drive also as a TimeMachine backup,

I will just use "person", to indicate You/your-daughter/that-paerson, who will work/configure these.

This person will need to go inside your NAS drive, & your daughter's NAS drive,

either via a direct/physical presence/keyboard,

or via a remote/internet connection (temporarily enabled inside NAS drive to configure, Do not forget to turn this temporary access OFF when config is done inside the NAS drive).

Then, that person wud need to RESIZE or REDUCE the size of, one of the existing partition inside NAS drive,

so that a new partition can be created for TimeMachine backup.

Strategy of creating new partition should be this : if your Mac computer's internal drive is 1 TB in size, then new partition inside NAS drive should also be atleast 1 TB in size.

Another way is, REDUCE the specified earlier SIZE of one of the existing shared-drive or shared-folder, inside the NAS drive settings, by 1 TB, if your Mac computer's internal drive is 1 TB.

I mentioned in above, both "partition" or "drive" based way , and also "share-folder-size-change" based way, ... because i dont know how you/your-daughter/that-person had setup earlier shared-folder / shared-drive inside your or her's Synology NAS drive.

After reducing existing one of the shared-folder or existing one of the shared-drive inside the NAS drive,

then that person wud need to create a NEW shared drive or new shared folder in the new empty or in newly available space,

which then can be accessed by using a new SMB resource URL, from your Mac computer (or windows computer or phone etc).

Find out your mac computer's internal/entire "Macintosh HD" drive's full size, by using "Disk Utility" software.

You said your mac drive is 500 GB.

EDIT :

i just found out, synolgy NAS drive/software does not allow existing drive's size reduction from their device UI webpage !!

https://kb.synology.com/en-global/DSM/tutorial/Shrinking_existing_volume

So 1st Buy/Get external USB drive (2TB) , that has storage capacity size same or higher than your synology NAS drive, you said your NAS is 2TB.

Connect your synology NAS drive's USB port/cable directly into your Mac computer, if necessary load synology software.

Use disk CLONING software, to clone NAS drive into the new USB drive.

See my earlier post here, & search for "Disk Cloning" in that webpage.

After you've done backup of your very important earlier all data in NAS drive,

then will need to RESIZE the partitions inside the NAS drive,

So you will need PARTITION handling / management software, that can reduce partition size (by 500 GB), from macOS.

Earlier mentioned "Disk Cloning" software may-be or should-be able to do this (partition handling) on synology drive (if they were also able to CLONE the NAS drive),

or, Get one of the macOS Monterey compatible & specialized partition handling software mentioned here & here,

you may need to contact partition manager software devs & ask, if itheir software can handle synology NAS drive from macOS Monterey.

Once you get such partition handling software, run that, that will be able to resize one of the partition inside your NAS drive, for you,

Apply this resize strategy : reduce NAS drive's one of the partition by 1TB , when your mac computer's internal drive size is 1TB , or , reduce a partition by 2TB if your mac's internal drive is 2TB, & so on.

Then detach NAS drive's USB cable, go inside NAS drive config page in NAS drive via WiFi / LAN connection, and create another partition for TimeMachine usage purpose.

By the way, if your NAS drive does not have sufficient space, to hold both your earlier "genealogy" data, and TimeMachine's required backup size , then you will have to change internal drives, inside the NAS drive, with other large size drives.

So for synology NAS drive related works, you will need to go to their/synology's community forum, or Contact their tech support directly if your synology NAS drive is within valid warranty period, & ask them to advise you on your need.

After above steps,

follow the rest of steps mentioned in next "Message 02 of 02" , here, in this page.

More info:

• 1. Back up your Mac with Time Machine - Apple Support
• 2. Other ways to back up and restore files - Apple Support
• 3. Backup disks you can use with Time Machine - Apple Support (Using NAS for TimeMachine).
• 4. Back up your files with Time Machine on Mac - Apple Support (Using NAS & other guidance, for Monterey, also has macOS selection change option).
• 5. Synology DS118 NAS drive documents.
• https://en.wikipedia.org/wiki/Time_Machine_(macOS)

Message 02 of 02:

... ( pls check "Message 01 of 02" here) ...

( you may have to reduce NAS drive's partition by : 500 GB + 1TB = 1.5 TB = 1500 GB , to create space for TimeMachine in NAS drive .

Because, you mentioned you have a 1 TB drive thats docking-station based drive, used from your mac computer's macOS (which has a 500 GB drive) , as part of macOS usage ).

After doing above NAS drive related config/settings/changes,

goto your macOS's "Finder" app > Go > Connect to server,

and specify the new SMB URL of your (LAN Network based network-storage) NAS drive's new shared-folder or new shared-drive's.

After that, that network-storage (NAS) drive will appear as a new-volume in your file-system / finder.

Then goto macOS settings > TimeMachine > Advanced > and use the network-storage based new-volume for your mac computer's TimeMachine backup.

... TimeMachine may format that space and create a APFS partition , if your mac computer's macOS is newer version , & if the NAS used GPT based partition/space . In some cases TimeMachine may also create a large sparsebundle file that has internal APFS filesystem.

... If your mac computer's macOS is relatively older version , then macOS TimeMachine will likely create older format HFS+ / HFSX / HFSJ ( aka: "Mac OS Extended" ) based partition , or a large sparsebundle file with HFS+ / HFSX / HFSJ filesystem inside it , to use as backup purpose from TimeMachine.

Another EASIER way to reduce external SMB NAS shared-drive's storage/partition size, is:

1: Find out what amount of important ("genealogy", etc) data you have inside the NAS drive.

Let us assume you have 400 GB of data.

2: Get a USB based external SSD or HQ (high-quality) flash/pen drive, that has atleast the size of your important data in NAS drive.

so, in this case, buy a 512 GB based flash/pen storage memory drive,

because your important data amount is 400 GB, so it can eaily fit into that 512 GB flash memory USB drive.

3: Turn on viewing options for all files & directories (including all HIDDEN files & directories) in file-browsing or file-management app "Finder" in macOS:

follow steps here.

4: Connect external NAS drive into Mac computer by using Thunderbolt or USB cable(s) , then load NAS drive manufacturer's software if necessary.

5: Also connect the USB flash/pen drive , into the Mac computer's USB port.

6: By using the "Finder" , copy your all important files & directories

from NAS drive , into inside the USB flash/pen memory drive.

So that, this USB flash/pen drive , can become your backup of all important files & directories from the NAS drive.

7: Turn off NAS drive, & again verify your USB flash/pen drive, if it actually has your all important data.

8: You told us , your NAS drive has total 2 TB storage space . 2 TB = 2000 GB.

9: Since Synology NAS drive's UI does not allow to reduce drive/partition etc,

and if obtaining a macOS Monterey compatible Partition-Manager or Volume-Manager or Disk-Cloning software is harder & relatively complex for you,

10: then SIMPLER SOLUTION is :

go inside the web-UI of NAS drive, and ...

11: DELETE all earlier data/partition/drive inside NAS drive , as you have already made full backup copy of important all files & directories (into USB flash/pen drive).

12: So now you can CREATE SUITABLE & NEEDED SHARED-DRIVE FROM BEGINNING :

13: 1st create a new shared-partition/volume inside the external synology NAS Drive,

that is NOT 2000 GB = 2 TB full size , but only 1500 GB size, Because this amount is needed, for backing-up your Mac computer, which has a 500 GB SSD drive, and to back-up the 1 TB (1000 GB) drive inside your (1st) Docking-Station, that is connected with your Mac computer.

This 1500 GB = 1.5 TB size SMB shared-volume inside NAS drive , will be used for TimeMachine backup software.

14: Then, create another/2nd shared-volume/partition that is using rest of the available storage space inside the NAS drive , it should be close to 500 GB . This 2nd SMB shared-volume inside NAS drive will be your external NAS drive.

15: Copy your all important files & directories , from USB flash/pen drive , into inside the 500 GB SMB NAS shared-drive.

16: If you do USB flash/pen drive steps in your side, to backup all data from NAS drive , then your doughtier does not need to do that,

or vice versa,

as making only one copy is enough, as both your data is synced-copy of other side.

17: But both of you must do NAS drive steps : delete all volumes/partitions, & again re-create based on what size volume you need.

18: Use remote desktop screen sharing software, with the person who will work on these.

19: When both, your & your daughter's NAS drive config/settings are done,

then you may have to again setup the SYNC (synchronization) options, in both of your 500 GB SMB NAS drive , so that both (your & your daughter's) side's files remain in sync.

20: then follow steps here (Message 02 of 02).

We need to view full filenames & full directory/folder(s) name , and we also need to view full file extensions & full directory extensions, etc, of all files & directories, etc in all drives very accurately , including HIDDEN ones , so that there is no mistake in file/dir copy/move operations , and something (hidden) is not-left out in source media, or not left-out in temporary media.

VIEW ALL HIDDEN FILES & DIRECTORIES, & THEIR EXTENSIONS:

• 1: Start "Finder" app in macOS : Finder is very similar to Windows-Explorer file-browser app/tool . In macOS > click on any empty area in Desktop screen > then goto top-side  menu, click on Window > click on Bring All to Front > then Finder window will appear in front of you on screen.
  • 1b: Hotkeys to start "Finder" instantly/quickly is :
    • 1c: press [Alt/Option⌥] + [Command⌘/WindowsFlag] + [Space-bar] then close the "Search" tab in Finder.
    • 1d: Hotkeys to start Terminal instantly : None : ( Note: Keep Terminal running: after a reboot, Terminal will auto-start if you check-marked the option: Load previous running apps after reboot ).
• 2: To start "Terminal", goto "Finder" > in left side, click on "Applications" > scroll-down & find & go into "Utilities" folder/directory > scroll-down & find & run the "Terminal" app . macOS Terminal is very similar to Windows Command-Prompt, a command-line interface (CLI) tool . Then run below command inside Terminal:

$ defaults write com.apple.Finder AppleShowAllFiles true

• • 2c: above command only makes the hidden files+directories viewable inside file-browser software "Finder" , above command does not actually change any file/dir attributes.
• 3: Then you must reboot Mac-computer OR run (any one of the) below command:

$ /usr/bin/sudo /usr/bin/killall Finder /System/Library/CoreServices/Finder.app

• • 3c: or, run just this:

$ /usr/bin/sudo /usr/bin/killall Finder

• • 3e: or, run just this:

$ sudo killall Finder

• • 3g: Then Finder will auto start, and all hidden files+folders will by-default begin to be shown to user in macOS "Finder".
  • 3h: In macOS Finder or inside any other file browsing window in macOS , user can also press below THREE buttons/keys altogether ONCE , then "Finder" (or file-browsing-window) will SHOW all HIDDEN files/folders:

[Command⌘/WindowsFlag] + [Shift⇧] + [.>]

• • • 3j: if user press-es above three buttons/keys again, then file-browsing-window will HIDE/invisible the HIDDEN files/folders.
• 4: By default in macOS, Finder will keep most of the "file extension" hidden . But we need to see all file's extension correctly & to see FULL filename,

so we can be sure & not make mistake, during file/dir copy/move operations.

• • 4b: To view all file's extension, do below steps:
  • 4c: in macOS > start “Finder” app > goto main menu > Finder > Preferences > Advanced > select the "Show All Filename Extensions" option.

Then all hidden files+directories will be shown/visible inside file-browser app/window,

and full file-extensions will also be shown/visible.

I am not familiar with those products so wouldn't be able to comment or predict. I don't know why you would need to "stack" docking stations, there are lots of high speed ports on a Mac Mini. What devices are you showing in the image?

quoting op "Could I stack 2 external drive docking stations and use one for backup and the other for additional storage? I am attaching an image of the device. How would I then backup the drive with the music and photos? Would that be a simpler solution?"

i know that such docking station do exists which can hold another docking station.

but such are rare.

and more rare for a specific mac computer.

not recommended.

but if if you have found one suitable & certified, then do use, if your need requires that,

(please provide power into each separate docking-station(s) with separate power-supply adapter).

when 1st docking station is connected in mac-computer,

then USUALLY you have to unplug all earlier cables,

or, the ports (usually THUNDERBOLT ports) that your (1st) docking-station will use,

you will have to free-up those ports, for 1st docking station usage.

2nd-docking-station which will connect with 1st-docing-station,

will also very likely again use the THUNDERBOLT ports of 1st-docking-station,

so you will have to move your existing Thunderbolt external devices, into the 2nd-docking-station's TB ports.

if 2nd-docking-station is not fully compatible with 1st-docking-station & mac computer,

then internal-devices, such as your 1TB drive, inside the 1st-docking-station, those internal devices will/may become inaccessible.

"backup" depends on other things: data storage size / capacity of drives, etc.

active device(s) or source device(s).

passive device or secondary device.

if the "Music & Photo" drive is 1TB,

then, To backup only that drive,

you will need atleast 1TB as a backup drive.

if "Music & Photo" drive is inside 1st-docking-station, & if its still accessible, after connecting the 2nd-docking-station,

then obviously you can make backup of "Music & Photo" drive from 1st-dock, into the 1TB drive inside 2nd-dock.

But not by using TimeMachine, by using a different backup software.

you may see this list:

https://en.wikipedia.org/wiki/List_of_backup_software

TimeMachine backup system, backups Mac computer's "Macintosh HD" & other drives connected in/under "/Volumes/..." ( if you enable backup those network-drive and/or those external-drive ) ,

into the destination of TimeMachine backup drive.

To backup a 500 GB mac drive, and to backup 1 TB of "Music & Photo" drive , by using TimeMachine software, the 2nd-dock's drive need to be atleast 500 GB + 1000 GB (1 TB) = 1.5 TB = 1500 GB, but best is to use a 2 TB drive for TimeMachine backup.