I installed Monterey on an external SSD on my m1 Mini (16, 512) on Tuesday. I mostly wanted to make sure that my third monitor worked (DisplayLink connection). It worked fine.
I reverted to my internal Big Sur boot drive. Today I noticed that Time Machine has not reported any updates since Tuesday. If I enter Time Machine, backups from Wednesday and Thursday are there.
I detached that SSD and tried another one. It's been at "Waiting to complete first backup" for five hours.
Time Machine still shows me backups from Wednesday and Thursday. Must be in some cache in the m1?
It's all pretty darned confusing. Was the glitch caused by installing Monterey on an external SSD? That SSD is detached and the m1 is running Big Sur from the internal. Or was the glitch caused by installing Big Sur 11.6.1 on Tuesday?
It's hard to say at this point. I can say that: in my case, The first initial backup had been done almost a year ago when Big Sur was newly out. I had at that time decided to start clean and switch from HFS+ to AFPS for TM backups as that was the new suggested setup from Apple. So, after upgrading to Monterey, time machine was running slow to make the new backup, so I decided to start clean again, as the drive had filled up, and the system was stable, and I didn't need the old backups. Also I have added considerable more data to the system since the first backup so the time needed to complete the initial backup would increase, but wasn't sure by how much.
Anyway, what I discovered was, by default when you setup a new TM disk, Apple also adds encryption for extra protection, which under Monterey really slows things down. So I reformatted, dismissed the notification for setup, and manually set up TM in the preferences pane. This time it's not encrypted, and while it did take a little over a day to complete the first backup, which was probably normal in these circumstances, it's been running normally since. I just checked this morning before posting, and the latest backup was reported done at about 5:08 AM this morning.
I will say this though, in the past, the more common time machine problems I've had are backups becoming corrupted, and having to start over. The two main causes in my case for this have been, old worn out drives, finally dying, or something going wrong when I was using the AirPort Extreme for TM backups. Now I just use a locally connected USB 3 drive.
If you are able to track down the specific cause of the problem(s) in your situation, let us know.