Touch ID is gone.

If Touch ID isn't working on your Mac

1. For Magic Keyboard with Touch ID, turn your keyboard off and on, then connect your keyboard to your Mac with the USB to Lightning cable. After you turn Magic Keyboard off then on, Touch ID may be unavailable for up to 10 seconds.
2. Restart your Mac.

There is an undocumented ( not that I have found ) but know, a Maximum of 5 Finder Prints can be stored on the computer.

If it has reached its' limit, remove some or all and start again with 1 Finger Print

Did you connect the keyboard to your mac using the cable, as suggested?

Does it make any difference if you start your iMac in Safe Mode?

On an Apple Silicon mac, the way to start in Safe Mode is different from Intel Macs:

Start up your Mac in safe mode - Apple Support

Does it make any difference if you create a different user account, and try to set up Touch id in that account?

(this is meant as a test, not a suggestion that you start using a new account)

You are welcome and thank you too.

Do come back to the Apple Support Communities ( ASC )  in the future, if / or when additional questions may arise

Wire the keyboard via USB Lighting Cable to Computer.

The the Touch ID in System Preference reappear ?

Manually turn Off the Keyboard, pause 5 - 7 seconds and turn it On again.

Does it reappear

From the View menu, choose Customize. Make sure that Touch id is checked.

👍 good one

Glad to see that it is working now.