You're welcome.
So the partition map has become corrupted for some reason. Your first instinct to reformat the drive was right on target, but as you know that does mean that everything on the drive will be wiped. Still have a couple things to try here.
Run First Aid several times in succession on the drive. Apple recommends repairing volumes first, then containers and then the drive. So... the volumes Macintosh HD - Data, then Macintosh HD, then the container and finally the drive device. Do this and see if there is any change in the end result.
How to repair a Mac disk with Disk Utility – Apple Support (AU)
If that doesn't fix things, try booting in Single User mode and run the FSCK command. It's a file system repair command. Boot the computer while pressing Command-S. When the Mac has booted into the terminal, type the following (noting the space) and press Enter:
/sbin/fsck -fy
You may have to run that several times until you get the "Volume Okay" response.
Then run:
/sbin/mount -uw
and finally:
exit
If fsck doesn't work then a third party drive repair utility may be needed. I've used Alsoft's Disk Warrior in the past. Maybe someone else can recommend another (?).
Otherwise, erasing and reloading the drive will be the way to correct this.
Also, I'd now question why this happened. So after you regain access to the drive I would recommend using DriveDX from Binary Fruit to evaluate the overall health of the device. Maybe consider replacing it with an external startup drive.