Utility disk error

If your Mac is running flawlessly, there is no need to do anything. Running Disk Utility to verify or "repair" the boot volume requires booting macOS Recovery: Use macOS Recovery on a Mac with Apple silicon - Apple Support.

Back up your Mac as a matter of course. To learn how to use Time Machine please read Back up your files with Time Machine on Mac - Apple Support.

I did a Disk First Aid on my Data volume on my M1 iMac today and saw the same warnings. I did a few reboots and rechecked but they were still there. Eventually, I booted into Recovery Mode and ran the same First Aid which saw the same warnings. Interestingly, after rebooting again, and running in the regular boot mode, the warnings all disappeared. It didn't say it fixed anything in Recovery Mode but they seemed to have gone away.

Keep in mind that while we can now discuss macOS Ventura, we still cannot publicly discuss anything that occurred during the Beta period. Those are development secrets which you agreed not to discuss. Only Apple and those actually participating in the Beta knows what the Beta OS had in it or could have done and still cannot be discussed here. A Beta test is more than just getting early access to software, so people should make sure to read the rules carefully before agreeing to using Beta software.

"Warnings" don't usually cause any problems, plus they are associated with APFS snapshots which will get deleted at some point. These may have been due to the Beta version of macOS you were running at the time. Even if you are now running the current public release, the Beta could have introduced some sort of issue. I also don't know whether you may still be receiving Beta updates as I have seen posts on these forums where you may need to remove your Mac from the Beta program so you only receive public OS updates.

Sometimes when you run Beta software, you may need to perform a clean install of the OS by first erasing the whole drive before reinstalling the OS and restoring your data (user account) from a backup.

Besides when First Aid is unable to repair the APFS file system, the only option is to erase the file system and restore from a backup since there are no third party utilities available for repairing an APFS file system since Apple has not yet released the necessary APFS documentation. Make sure all of your backups have successfully transferred to your external media which should cause macOS to delete those APFS TM backups. It is possible to manually delete APFS snapshots, but if those TM snapshots were never successfully transferred to external media, then you may lose some of your backups. Do this at your own risk:

View APFS snapshots in Disk Utility on Mac - Apple Support

https://derflounder.wordpress.com/2018/04/07/reclaiming-drive-space-by-thinning-apple-file-system-snapshot-backups/

FYI, never run Beta software on your main system as you never know what problems it may cause. It is best to only run Beta software on a second system (or possibly an external drive although the system firmware will have been updated which could cause issues).

Ventura is no longer beta OS. These errors are compiling. Similar errors appeared in Monterey and Catalina.

AFAIK, Ventura is still considered a Beta OS that has not been publicly released yet to the general public so you are not allowed to discuss any issues with the Beta software as per the NDA you agreed to when downloading & installing it.

Also, I'm not aware of Apple releasing the necessary APFS documentation yet so that any third party utilities can repair an APFS volume.

Unfortunately I got an error message that the drive could not be verified after completing first aid with the recovery option. I'm not sure if it is the primary hard drive or the Time Machine backup that causes the error. I do know that a two year old Apple Mac Pro already required two graphics card replacements, a motherboard replacement, a speaker replacement and assorted other repairs. At least it us under Apple care, but one of the least reliable computers that I've owned.