First Aid from Recovery failed: reinstalling Ventura didn't correct this

Was First Aid run from Recovery Mode? If not, then do so now to see if it will fix those errors.

If First Aid is unable to fix those errors while booted into Recovery Mode, then you will need to perform a clean install of macOS which involves first erasing the drive before reinstalling macOS & restoring from a backup. I've linked the Apple instructions for using Disk Utility to erase it which involves the "Volume Group". If you have a 2018+ Mac, then you also have the option of a firmware "Restore" which will erase the internal SSD and prepare the internal SSD for macOS (2018+ Intel Macs will still need to reinstall through Internet Recovery Mode).

Ewan Lamont wrote:

I am puzzled by the fluctuating lists of "volumes" in Disk Utility

If you boot from a macOS installer, then there will be a lot of virtual volumes shown which the installer creates & uses.

and the changing number of Snapshots shown which yesterday reached 19. The Snapshots list is down to 9 but that is higher than it usually was.

No idea, but three possibilities....one, a backup drive hasn't been connected long enough to transfer the backup snapshots. Two, maybe backups are configured to run a lot more often which means they you will have more of them sticking around until their timer expires so that macOS automatically deletes them (or whatever backup software is being used). Three, maybe some other third party software is creating snapshots....in that case who knows what their rules are for creating & deleting snapshots. I've never had time to pay attention to this detail.