Password works for Login but not for Security & Privacy Preference

Today, I found that the Login/System password on my MacBook Air works for Login after sleep or restart, but does not open the padlock of the Security & Privacy preference. The password is rejected with a shake.

About the same time, I found that Touch ID was no longer working. I deleted the old fingerprint and tried to add a new fingerprint. My Login/System password was accepted, but nothing happens when I click the "+" to Add Fingerprint.

I upgraded both my iMac and MacBook Air to Big Sur about a month ago. Since then I have rarely used the MacBook, but use the iMac daily without a password problem.