My F1 key stopped working on iMac with Monterey

Please restart in Safe Mode. Below are some instructions to follow:

1. Shut down the computer normally.
2. Unplug ALL wired peripherals (USB, Firewire, Thunderbolt, etc....) from the back of the Mac.
3. If you use an Apple wireless keyboard connect the charging cable that came with the computer to the back of the iMac and the keyboard. If you use an Apple keyboard that uses replaceable batteries, plug in ANY USB wired keyboard.
4. Restart the computer and hold down the Shift Key until the computer fully restarts, this may take up to 10 minutes.
5. Restart normally and test the keyboard that is having the issue.

Additionally give this a try:  Reset NVRAM or PRAM on your Mac - Apple Support (for Intel Macs) and Mac startup key combinations - Apple Support (for both types)

and

How to reset the SMC of your Mac - Apple Support  

Keyboards sometimes last 20 years some 5 but try OTs suggestions too, they might do the trick.

if you have another keyboard handy, try it and see what happens. If the problem goes away with a keyboard change then yup it’s the keyboard.