I know this thread is over a month old, but I just came across it. I had a similar problem that Disk Utility (DU) said it couldn’t fix. After doing some research on line I found the thing that worked for me. I posted my experience in Apple Community, but the essence is this:
Run DU (Disk First Aid) starting with the last/bottom volume in the list of volumes shown on the left (e.g. Macintosh HD - Data) and working your way up. Once you’ve run DU on the next volume (your system volume, e.g. Macintosh HD), the next step is what surprised me. Move to the text that says ‘View’ with a down-arrow that’s just to the left of the words ‘Disk Utility’ in the top of the window and choose 'Show All Devices." This will reveal the ‘Container’ that your volumes are in, and the ‘Media’ (actual hard disk/SSD) in your computer. Run DU on the Container first (which might take a long time), then run DU on the Media. Running it on the Container fixed my problem. I didn’t find any problems on my Media. After that I ran DU on my ‘Macintosh HD - Data’ where I had gotten errors before and it had no errors. Hope this helps.
BTW, on my Mac running Monterey macOS 12.6.1 DU can now check and repair the volumes on my backup external drives (clones). For a long time DU wouldn’t work on external drives but it does under 12.6.