Admin authentication not working on Big Sur
I would make a second admin account, maybe something simple and insecure like me/me and then try to see if the problem is your account or if you can open it with the “me” admin.

First test when your old account is logged in, when the admin prompt arrives, change your user name to me and use the “me” password.
Then log out as you, and see if me can unlock their account.

This sort of thing is hard to guess from a far, but easy to corner and once you have a cornered you’ll know where the problem lies. Everything you mention is explained by a corrupt user preferences (or worse, failing filesystem) so be sure you back up all your critical files immediately and get a Time Machine or whole system backup sooner rather than later.