After a security update, I encountered the same problem that I was not given the option to use my Touch ID to log in on my Mac. I had to go to settings. The option to use Touch ID was set already. I had to un-check the option and then went out of settings. Later I went back and checked the option to use the Touch ID. Then I shut down my Mac, gave it 30 seconds and restarted my Mac. When I could log in again, the option to use Touch ID worked again. I have tried locking my screen several times, Touch ID still works. PS: I do not have OS Big Sur, but Mojave 10.14.6.
MarianneV
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