Macbook Pro 16" M1 not recognising apple extended usb keyboard

Ok first check to see if it's drawing too much power. Unplug any other devices in your thunderbolt 4 ports.

Check the ports on your keyboard make sure no mouse and/or usb stick other usb devices are connected in the side usb-a ports. Both the left and right side. Unplug any extra devices. See if just the keyboard standalone works. Next power off the machine. Hold the shift key while powering back on the machine to boot into Safe Mode. Next use your credentials to login. Once logged in connect your keyboard again to see if it is recognized in Safe Mode. test out the keys make sure everything is typing correctly. If not then turn off the machine again. Perform an SMC reset by holding the ctrl+option+shift+power keys for 10 seconds. Then reboot see if it is detected this time. If not then it's time for a final drastic step. Leave your keyboard plugged in. Power off the machine. Hold cmd+r simultaneously as you hold the power button to power up the machine. Release the keys once you see the apple logo loading splash screen. Next you will boot into Recovery mode. Next click Install macOS Monterey. Don't worry your data and apps will still be intact. At this point you have to install a copy of the os again on top of the current os to correct any major core components that may be messing with your hardware profiles. Upon reinstall boot the machine again and see if it is detected. The final step is not a pretty one if it's still not working at this point. I would honestly recommend going out and buying a bluetooth magic keyboard to save from hassle. But if you want to go through with the alternative then it's time to do a full back up of your machine. Turn off the machine. Boot into recovery mode using the same instructions from earlier cmd+r+power. Then open disk utility. Select your start up drive, most likely named Macintosh HD. Once highlighted select the option in the right pane "erase". Now this will erase everything, and you'll install MacOS Monterey from scratch. So next exit out of Disk Utility and this will return you to the Recovery Mode screen. Next select Install macOS Monterey. This will take roughly an hour of time. It will be a fresh install. I recommend leaving your keyboard connected while it's doing this. It will take roughly 20 minutes from the first installation stage. Then when it reboots it will say it takes 40 minutes to complete the installation, but based on your hardware it will probably take closer to 25 minutes in the second phase as this is usually just an estimate.

Best of Luck!