I have the same problem with my 2017 MacBook Pro touch bar model; updated to Big Sur and started experiencing the frozen screen and mouse issue. Erasing and reinstalling the OS did not work (I tried at least 5 times), waste of time. Got "Genius Bar" appointment, the representative initially said its trackpad issue and used some diagnostic tool. Everything green, no issues found. They agreed to reinstall Big Sur and check one more time, it didn't help. The representative said its a kernel panic, need to replace the logic board.
As a last option, I asked them to install High Sierra on my machine and it worked without any issues.
It is very disappointing that Apple was not able to provide any solution for this problem and "Genius" team tried to replace the logic board for the software problem. They were not confident on their suggestions, first said trackpad issue and later switched to Logic board issue. I didn't see any genuine interest in them to fix this issue. Unbelievable and unexpected from Apple.