2 questions

You have NOT actually partitioned the Drive.

In fact the drive you partitioned is most likely the Backupbundle. (more correctly called a Sparsebundle but apple changed the terminology to confuse us).

To check..

Please dismount the TC drive in Finder.. This will dismount the Backupbundle as well.

Then mount the TC drive again.. do not mount the Backupbundle.

Check what files and directories you have.. It should be a couple of small Apple file location data info and just the Backupbundle (unless you copied other files and / or folders onto the TC drive). This will mean your partition is not real.. you have partitioned a virtual disk. What you should have done is create a DMG file directly on the main Data share and place all your Photos libraries inside it. But even this is not a backup.. so copying to external USB drive is essential and should be done immediately.

Please turn off Time Machine NOW until you have managed to recover your files.

What has happened with permissions is the Time Machine has permissions over Backupbundle and everything inside it. This is desperately dangerous for obvious reasons.. Time Machine could corrupt itself tomorrow and it will delete the existing Backupbundle and start over with a new virtual disk. This will completely remove your secondary virtual partition inside the Backupbundle.

To copy the folder out of your virtual partition you will need to use command line copy commands with sudo in front.

OR fix the permissions via old airport utility. (5.6.1) which will require either using a PC with 5.6.1 for windows.. or loading the special script into your current version of Mac OS.. in theory works up to Catalina.. but people do have issues. We are not allowed to give URL so just type in google. launcher 5.6.1

Once you have a working 5.6.1 utility (install and once you change the permissions uninstall it) the solution is easy..

Go to the Disks tab, File Sharing.. by default Airport Disk Guest Access is Not Allowed.. change it to Read and Write.. and click update. This will work but does ultimately reduce the security on the backup. Changing back to Guest access off.. is not something I would recommend.. unless you archive the TC before doing any of this.. which is well worth doing before you start if you have no backup for these photos. NOTE that time machine will not be backing up your photos on the TC.. that is impossible.

Just to add there is no way to actually partition a Time Capsule drive without removal of the drive from the TC.. partitioning it on a Mac and putting back in the TC. This will always give disk errors in any of the later OS.. we used to get away with it long long ago.. galaxy far far away.. you get the gist.

Woo-hoo! I used a copy of Airport Utility that I had on an old Powerbook (1.67 ghz), vers 5.4.2. Changed the File Sharing setting and now I am able to copy the photoslibaries onto my MBP and onto the LaCie drive (or directly to it, haven't tried that yet.)

Well done.

If you plug the LaCie drive into your computer's USB then copy the whole folder of content from TC to the disk in one go should be no problem.. and not even have any slow down. Don't copy to USB plugged into the TC.. as that involves a double copy of files across a wireless network and will go much much slower.

Great using the old Mac.. Apple eliminated a lot of useful tools in the so called Airport Utility... !!

Going into Time Machine, all of my backups are in red

This is normal.

Some backup dates might be bright red and others appear as a pulsing faded red color. The bright red dates indicate that data can be restored from that backup immediately.

Faded red means that the data in the backup has not been fully loaded, so that backup will remain unaccessible until the backup is fully loaded. This may take some time, especially if you are accessing the Time Capsule using a WiFi connection.

How is it a double copy?

Sorry what I mean is double copy over network.

ie.. all files are first copied to the computer from the TC.. Then they are copied from the computer back to the TC and then copied to the USB drive. Wireless is very good at one way data traffic.. really lousy when data (exactly the same data) is going both ways. This is much less of a concern on ethernet which is duplex.. i.e. it can send and receive at the same time.. wireless cannot.. it is half-duplex.. meaning it can only Tx or Rx .. which means there is huge delay and speed is half.

What other ones would you recommend.

The old airport utility has log readout.. new version none.

The old airport utility can record all connections.. new version only wifi.

The old airport utility gives you more info and control over USB printers.

The old airport utility has much greater control over front led indications.

The old airport utility has proper DHCP table and listing.

The old airport utility can store and recover multiple configurations. Completely gone in the new version.

Lots more.. people have simply learned to live without. But I actually want much more advanced controls as even the old utility was poor compared to 3rd party routers I use now. Why don't they have advanced section for people who actually understand what they are looking at? It is all withheld to ensure yes and no answers from support.