I have the exact same problem on my M1 MacBook Pro 13".
I have an admin account and after downloading 11.2 it asks for my password to restart. I enter it correctly, and the dialog box just shakes as if I entered it incorrectly. I do it again, ensuring it is correct. Once again, it won't accept it.
I tried what you suggested by changing the password. Same thing. Other functions where I enter my password work correctly (logging in, creating a new user, updating apps, etc).
I also tried creating another user with admin rights. Same problem.
I've tried resetting the SMC, no luck. I've tried booting in to safe mode, no luck.
How do I fix this?