the one I am using on my Mac Book Pro (OS Sonoma 15.3) is working fine. Are you saying that one is going to stop working ..... maybe the next time I upgrade OS?.
That's part of the confusion MS created with the upgrade options for Mac users. The 2021 version will only activate under Mojave, Catalina and Big Sur; per Microsoft's own specs of only three major Mac OS releases from the time a perpetual version is released.
Once you pass that third OS, what you have will keep working since it's already activated, but supposedly won't let you apply any more updates. For the one that stopped recognizing its activation, you can't reactivate it since the OS version is beyond what the 2021 activation servers will allow.
The last official update for Office 2021 (according to MS's update page) was back on February 16, 2022.
Do you have any older backup files for the non-working Office 2021 install of the user account /Library/Group Containers subfolders? There are several created by Office. Besides all of your Outlook data and other app settings and files, the files that tell Office it has been activated are also in there.
You have to be careful about bringing in old folders like that, if you can find them. Mostly so you don't lose your current Outlook data, which may have newer information in it than are in the backup files.
Unrelated. Shouldn't I be getting OS update notifications on my iMac?
The OS will only tell you when the OS, or installed App Store purchases have updates. Office is supposed to keep track of its own updates and inform you if there are any. If for some reason it hasn't been, you can go to the Help menu from within any Office app that's open and choose the option to check for updates.
When you do that under Sonoma, Office may very well inform you that updates are no longer available under the version of macOS you're running. In which case, just cancel out.