I had to do two things to make touch-id work. I am running a MBP 2016 and upgraded from Catalina to Big Sur 11.1 today.
FROM: https://support.apple.com/en-ca/HT201295
Shut down your Mac.
Press and hold the power button for 10 seconds, then release the button. (You'll hear a quick swoosh)
Wait a few seconds, then press the power button to turn on your Mac.
THEN!!!! You must enable unlocking here:
Re-enable "Unlocking your Mac" in System Preferences -> Touch ID.
Apple, this appears to be a common problem.