TimeMachine Migration Issues

We are upgrading my wife’s 13" MBP (mid 20120) running OS 10.14.x to a 2022 M2 “Air” (OS 13.2).
Using Migration Assistant. Things wen fine until… TM tried to update (hourly) but could not complete -“not enough space”. The problem appeared to be that TM was unable to remove the oldest backups to make room for the latest. After going through the recommended remedies on Apple & checking with the user community, (no joy) we called Apple Support. Spent some time with the first line assistant, got "promoted’ shared screen etc., His diagnosis was that the problem had to do with the fact that the new M2 silicon used APFS format which was incompatible with the previous TM backups. The best he could suggest was to erase the old backups and “start anew”.
I found this idea problematic 1) the whole point of TimeMachine is to preserve history --particularly useful after migration 2) I have migrated from a similar vintage MBP to a M1 Mini last year and still have access to a few months of pre-migration data on TM . (My wife’s ™ is on a remote (USB) HD -1TB partition.) On inspection of this partition, it appears that there is an ‘old’ backup folder and there is an incomplete attempt to add a new backup folder with a file “in progress”.
Has anyone came across this problem? found a solution? or figured out how the OS is dealing with the difference between the old & new types of backup?

I encountered the same problem but could not solve it.
I ended buying a new external SSD and using that for TM with my M2 Macbook Air. That is, it does not have old backups.
The old TM SSD that I used for the migration is now an archive (ie not used for TM) but is still accessible with the old Mac.
Now that you have raised the issue I might try accessing the old SSD from the TM app on the M2 Mac to see if it can restore an old file.

I was wondering about doing the same Michael; I copied the file from the T M to another drive and thinking of using it with the ‘old’ MBP -which we keep for spare. But I suspect that in my M1 Mini the T M is somehow able to delete the oldest files thus have a ‘seamless’ app. 2 year history I can access easily -without going back to the older machine. -This is what T M supposed to do…

Not the exact situation, but after a discussion here, I did realize I was considering TM backup drives to be more precious than I ought to. Meaning, HDs are cheap, a TM backup drive that’s running out of space is not keeping much of a backup history anyway, and if I keep the old drive (with a nice big label on it), I can start over on a bigger drive pretty much with impunity. On the off chance that I need something from before I switched, I can easily switch drives.

“Icing” the old T M is a partial solution at best -you need to know the exact date of what you need to determine which version of your T M you would need to access to recover. Also, if the problem is in fact the incompatibility between the old & new filing system, your Apple silicon Mac may not be able to access the “old” T M files… There ought to me a more elegant solution (IMHO)

BTW… Creating a new TM backup to SSD with the new MBA was much much faster than with my older Macs. So having multiple drives for TM backups and creating a new backup from time to time is less inconvenient than previously.