I’m experiencing this issue and have opened a case with Apple support. It took ~30 min on chat with the entry-level support person, and then 1 h 43 min with the senior support person the next day. That got me to the point where they were able to confirm the issue and collect data from my machine (2021 14” M1 Pro MBP). The senior support person confirmed that others have reported this issue (TM appears to complete a backup, but then reverts to the “Waiting to Complete First Backup” state). He couldn’t speculate on a timeline for resolution. He told me he encourages everyone experiencing this issue to log it with Apple to raise the issue’s profile and allow them to collect more data about the problem. (Just passing that on—I realize not everyone has 2.5 hours to spend with Apple support, and we all wish they had not broken TM in the first place.)
Just to be clear, the issue I’ve experienced is: starting with a newly reformatted backup drive and macOS Monterey 12.1, Time Machine acts like it’s successfully making an initial backup (it takes 1-2 hours; progress bar goes from 0% to completion; status is briefly “Cleaning Up,” etc.), but then reverts to the state it was in before the backup was started (“Waiting to Complete First Backup” in menu bar drop-down; Oldest backup: None / Latest backup: None in TM preferences). No backups appear on the backup drive in Finder, but the used space on the backup drive increases by about the expected size of the backup. Subsequent backups take some number of minutes or hours to complete, but end with the same result, until eventually the backup drive fills up. When I point Migration Assistant to my backup drive, it doesn’t find any usable backups. I’ve tried two different backup drives (an SSD and an HDD), reformatting the drives, running the backup in safe mode, reinstalling the OS, and running First Aid at all levels of the various disk hierarchies. None of that has helped.
The one change that has allowed me to successfully create backups is excluding /Users/[username]/Library from backups for all the users on my machine. I haven’t tried to narrow the exclusions down any further than that. Not a solution, but it allows me to create some kind of backups. (In the TM logs, I’m also seeing what appear to be error messages related to files in /Users/[username]/Library/Containers, and backups appear to be failing with the code “BACKUP_DELAYED_UNFINISHED_PROTECTED_FILES”.)
I appreciate the work of folks who have already looked into this issue and have provided suggestions. I will continue pursuing my case with Apple support (and hope others do the same), and will report back if I learn anything useful.