Unfortunately, I've personally observed these issues becoming somewhat more common since around the time macOS moved to APFS but Time Machine remained HFS+, although I am not sure if that is related or not. I do not have a great solution here, as Time Machine issues seem very difficult to diagnose and fix, but there are a few things I can think of trying if you have not already. (I am assuming you have already performed First Aid on both the Mac's local drive and the Time Machine Disk.)
One option is to first make a Carbon Copy Clone of your current (malfunctioning) OS on the local Mac drive to a completely separate drive. Then at that point you have a few options. One option is a fresh install of the operating system followed by another attempt to perform a Time Machine restore with Migration Assistant. There are no guarantees this works, hence the need of a clone backup of your current disk (so you don't lose your files.) It will necessitate you to reinstall some software if it is successful, and more if it is not (i.e., if it fails, it will be like setting up the system when new...but this should resolve your issue provided it is not related to hardware failure.) However, if this is successful and the problem you are experiencing is induced by a specific app or setting, it could be copied over.
You can attempt to repair the Time Machine backup with an application like DiskWarrior to try to fix potential directory corruption that may prevent a successful restore. Again, no guarantee of any success.
You can also run a SMART check of both your Mac's drive and the backup to drive, to see if either are physically failing--sometime this can cause freezing behavior or could prevent a successful restore.
You can run Apple Diagnostics to check for other component failure on your Mac.
At the end of the day, I hate to say it but the most likely solution is the longer one of a fresh OS install, manually reinstalling software, and then transferring your files over from a clone or a backup of user files. Moving forward, a large hard drive with multiple partitions for multiple complete (and bootable) clone backups at different points in time is often a more reliable backup solution should complete restores be desired.