Mysql Daemon cannot start after upgrade from 5.1 to Mysql 8
That is a gynormous upgrade.

Plan A:  Oracle recommends doing it in 4 steps 5.1 -> 5.5 -> 5.6 -> 5.7 -> 8.0.  And, at each step, run mysql_upgrade.

Plan B:  Alternatively, you could dump the data and hope that the reload doesn't find some syntax errors.

I fear that you may have already hosed the files too much to have a successful upgrade.