Touch ID has stopped working on my iMac

I noticed a week or so ago, possibly since the last software update, that Touch ID had stopped working on my iMac. I have tried setting it up again using System Settings > Touch ID & Password but each time I get the same error message, “Unable to setup Touch ID on your keyboard”, and the option to set up Touch ID disappears until I restart the iMac.

The chip is an Apple M1, 8GB and operating system is MacOS 14.2.1. According to System Settings > General > Software Update there are no outstanding updates.

I have tried using Apple Diagnostics (from Use Apple Diagnostics to test your Mac – Apple Support (UK)) but the power/Touch ID button on the keyboard doesn’t seem to be working (nothing happens if I keep it depressed for over 90 seconds) and if I restart using the power button on the back of the screen but this just starts it as usual without offering the startup options.

Does anyone have any suggestions of what I can do next to fix this?