iMac won't boot

It is generally a good computer practice to alway keep at least 15% to 20% of the Total Drive Capacity’s as Empty Space.

Allowing the computer to drop below these guidelines may eventually, cause unintended consequences including what the computer is experiencing now.

There is Purgeable Space and there is Empty Space.

Purgeable Space which is Controlled by the Operating System. When the Operating Systems decides the computer needs additional Empty Space, it will move a portion of the Purgeable to Empty space

AFAIK - there is no User Actions to hasten this transition from Purgeable to Empty Space

It can day or longer before this will occur  

The links below will assist in identifying what is taking up space on the Internal Drive and provide possible ways to remove data that is under the direct control of the User ( Home Folder ) . 

Rebuild the Spotlight index on your Mac

What is “Other” storage on a Mac, and how can I clean it out?

Free up storage space on your Mac

OmniDiskSweeper Safe to use

GrandPerspective 

➡️ How to delete Time Machine snapshots on your Mac.  

Often caused if the Time Machine Drive has not been attached  to the computer and TM Backup is set to run on a Schedule. 

TM Backup will make Snap Shot on the Internal Drive awaiting the TM Backup Drive to be attached. 

Only then will the Snaps Shots be transferred to the External Drive and deleted the Internal Drive. ⬅️

See used and available storage space on your Mac

Locate backups of your iPhone, iPad, and iPod touch

Notation - If the user is using a cloning software like Carbon Copy Cloner - and https://bombich.com/kb/ccc6/automated-maintenance-ccc-safetynet-folder suggest tweaking the Safety Net Feature in this software. It may be making additional Snap Shots that are not being Cloned to the Eternal Drive. If this should be the case, these Snap Shot could be using additional space on the drive 

If this computer has many Adobe Applications installed, suggest checking with Adobe on how to remove their cache files

Have seen some users that discover, Adobe cache files can occupy many GB of space on the drive.

The final word from Apple on Managing the " Other/ System Data “ Category

Other / System Data: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

Does that mean my only recourse is to wipe the main drive and reinstall Ventura from scratch?

Yes.

Follow Apple's instructions, as you quoted:

"You must use Migration Assistant to transfer data from this backup. Reinstall macOS if necessary and then use Migration Assistant to transfer data from your backup."

... but you have to erase the startup volume first, since Disk Utility cannot "repair" it.

That's the way it's done these days.

Is there maybe a way to use Terminal to delete some files and create enough free space for some of these steps to work?

That's a moot point since Disk Utility is unable to effect repairs. Deleting files and creating more space will not fix the corrupted startup disk. Only reformatting it can do that.

By the way none of this has anything to do with the amount of data the startup volume happens to contain. You did nothing wrong. Go ahead and fill up your storage. That's what it's for.

Then there is >>

This method will WIPE ALL Data and there is No Recovery - Period.

>> Only works on Intel Based Apple Computer <<

To perform this action will require booting from a Bootable Installer. 

The Bootable Installer can Only be performed on an Apple Computer 

This will have to be performed from a Qualifying Computer to run the version of macOS to be made on the Bootable Installer. Example : Bootable Installer of Big Sur would have to be done on a computer that Qualifies to run Big Sur.

Notation: If the computer being used to perform this action is Too New or Too Old to qualify to run the version of macOS - this computer can not be used.

Alternative is, to gain access to a Qualifying Apple Computer from a family member, friend or associate.

1 - Shutdown computer and disconnect all external drive Except the newly created Bootable Installer.

2- Restart and immediately hold the OPTION key until the Startup Manager appears and choose the USB Drive. 

3 - It will present options >> Disk Utilities >> View >> View ALL attached Drives. 

4 - Choose the Upper Most Drive ( not the volumes indented and list below ).

5 - The drive normally is called Apple Media or Apple SSD - that is the drive to Erase and format as APFS with the GUID Partition Map. This applies to macOS 10.14 Mojave and above. 

6 - Once that is done >> backup out of Disk Utilities and choose install macOS. 

7 - Follow the prompts and it may automatically reboot several time. 

8 - Upon a final reboot - Setup Assist will present with the newer version of macOS.

What follows is only a personal opinion.

Mucking around in Recovery Mode >> Terminal to try and make space on the drive can be difficult.

One wrong thing in Terminal may render the machine Totally Non Bootable even getting into Recovery Mode.

As was implied earlier there is a Time Machine Backup existing

The machine and user ( you ) might be better off WIPE ALL Data via the Bootable Installer method

Then, using Migration Assist and  migrate Only User Account and nothing more.

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and, if possible, run for a bit. Reboot normally and try again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

If you get booted up find out how much free space you have. If plenty then check out this Apple document: If your Mac doesn't start up all the way - Apple Support

Welcome.

Before going wipe and reinstall route >>

Transfer files between two Mac computers using target disk mode - Apple Support (CA)

muckster wrote:

Thanks, but I don't think I have the Thunderbolt cable to make that work.

Is there no way to use Terminal in Recovery Mode to delete some files off the non-booting mac?

That last part in above kind of answer your question

If the machine is Non-Booting that infers one can not get to Recovery Mode and use Terminal to remove files

1 - Restart in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Safe Mode will also eliminate Third Party Software, extensions and drivers from loading. It will only load the Minimum amount of Core Apple Processes to allow the the computer to function at a reduced Level of Performance 

Perhaps in this mode, if it should boot up at all, may give you enough latitude to do some " housecleaning " 🤞

The Only area you would have Direct Control over would be the Macintosh HD-Data Volume

That is where your User Account ( Home Folder ) would be located in a normal boot up

I am sorry by friend but user wrote " This is the same for all my TM backups. "

The use one of those to restore from