Can't use admin login

Following an ill-timed upgrade to Big Sur my wife's MacBook Air is almost unusable. There are apps she wants to upgrade and we can't login to an admin account. She is the only user and has the only login and used to be the admin, but now has been changed to standard. We can't change back to admin because we don't know another login name for Administrator let alone a password. The apple store where we live is closed, I think forever. So we are on our own at present.

When we try to reboot the system hangs. We have to perform a hard shutdown, use a cmd-option-R-P to clear some portion of memory, another hard shutdown, and then boot while holding down the shift key. Then it will sometimes log us in under her standard account, but with many pieces not working.

Can anyone offer advice on how to setup or recover the system admin name and password?