After a couple more 'chats' with AppleCare it came down to the suggestion of remove all of the non apple applications and try the TM backup. I suggested that a complete clean install may be quicker and easier in the long run. It would get rid of everything migrated from our old iMac.
So the bloke talked me through the erase and reinstall until it was well underway. I finished of the install and tried a TM save and IT WORKED!
Then I ran TM after I put each application back on the system SSD. I thought it would take forever, but as it's now running correctly all it did was add the applications just loaded. I now have pretty well all of the applications loaded and all still seems to be well.
Having read that, and having nothing else to do on New Year's Day but watch the bowl games, I decided to do a reinstall myself to see if that fixed my problems with TM. To review, TM runs, space on the destination drive is taken up, TM ends with no errors but the target drive has NOTHING on it, but space is gone. First Aid doesn't find anything wrong with the target drive. Showing hidden files doesn't disclose anything on the target drive. Examining the logs, I see an error message like this at the end of the TM run:
2022-01-02 01:31:31.256805-0500 Backup failed (104: BACKUP_DELAYED_UNFINISHED_PROTECTED_FILES)
So, I took the plunge, made a clone with Carbon Copy Cloner and then invoked the "Erase All Contents and Settings" from System Preferences. Got the warning that it was going to log me out of AppleID, Find My Mac, etc. Went ahead with it.
On booting, went through the "hello" and setup phase, set up an account and tried TM on a new drive. Bingo! Good TM backup, files show on the target.
Used Migration Assistant to get my stuff back from the clone I had made. Was happy that it all looked so good, until.....
Tried a TM backup. Same results as before, space gone, no files, no way to recover files, same error message in the log but no error from TM. So, it's something in MY files, or MY settings. At least I now have something to work with.
Cue foreboding music...
A couple of hours after I had successfully added my cards back to Wallet (They are not restored from backups for security reasons) I get a cryptic notification that Wallet has been disabled and my cards removed because of the security change to my system. Wha? Tried to add them in again, got this popup:
The Learn More button took me to a Apple page that said my system wasn't secure enough for storing cards because of a change in the security (I didn't make any changes) or because of malware. Ran DetectX Swift and VirusBarrier scanner, nothing found. Called Apple, was told that I had to talk to "specialists" and that they would call me later today. Here is what is curious. I went to the AppleID management site, it lists my MBP as associated with my account and that Wallet is authorized with the cards I have on my iPhone and Watch. So, one Apple systems says "no" and another says "go." Could be an interesting call.
So, the "fix" didn't fix TM and broke Wallet. The call is scheduled for about 40 minutes from now. I'll report back, assuming I'm not in the erase-restart-recover-lather-rinse-repeat cycle.