Sturg, I can fully understand your paranoia but you did have a hardware replacement which does seem to indicate something other than just a software problem but because you were able to boot in Safe Mode it's also possible there was a software issue too.
I guess your problem boils down to, what do you actually
need off the TM backup? If there are essential or important files then by all means restore
them but I'd be inclined to shy away from applications/utilities. If you really want an application then download a fresh copy from the developer (not a secondary source).
If you restore things a few at a time you will be able to identify and remove them if you do encounter a problem.
I'm running the same device you have, a 2021 14" M1 MBP, my software and files are a product of a wireless Migration from a 2015 13" MBP. I have never had a problem like yours although I have had hardware issues with keyboards and batteries in the past.
Over the years I have regularly performed "clean" instals of new versions of macOS. Although not so necessary nowadays it was a good way of getting rid of old redundant software and leftovers.
Essentially this meant booting from another source, erasing the internal HD, installing the new macOS then restoring all of my files from the clone and applications from the app developers. That's pretty much what you have done.
I preferred a clone rather than a TM backup for this purpose because the structure looks the same as the internal HD. Below is a screen shot of a CCC clone of this HD.
As you can see it is simply a Finder window. I could drag anything from that to the desktop of my laptop and it would be moved there or I could use Migration assistant to restore some or all items as part of a new instal.
The point is a lot of the data it is unnecessary. I don't need, for example, to restore my Library, System Library, Users or Previous content. Things like the Application Support library, Helper Tools, Graphics, Installer Sandboxes ect ect all get created anew as required.
Just my personal files and applications need restoring. Yes, I have to reset my System Settings (Preferences), Permissions, System Files access ect. but this is a good way of reviewing them and in some cases removing them.