After upgrading to Monterey unable to login on Mac mini

I had this exact problem when upgrading from 12.7.3 to 12.7.4. I don't have a permanent solution, however I did find that if I SSH into the stuck machine and kill the loginwindow console process (/System/Library/CoreServices/loginwindow.app/Contents/MacOS/loginwindow console) that when it restarts, it accepts keyboard input, and I am able to log in. I am now afraid to reboot.

Try booting into Safe Mode to see if you can log in. If this works, then you most likely have third party software installed which is interfering with the normal operation of macOS.

Or if your Mini uses a hard drive, then perhaps the hard drive has failed. Many times a macOS upgrade will push an old hard drive over the edge revealing it was already at the failing point. You can try running the Apple Diagnostics to see if any hardware issues are detected, but unfortunately the diagnostics don't detect most drive failures (or most other issues for that matter).

Also make sure to disconnect all external devices in case one of them is causing a problem. Of course you will need to have a display connected and perhaps a USB wired keyboard.

If you have a spare USB3 SSD, then you could try installing macOS to the USB SSD (or hard drive, but a hard drive will be slow) which will provide useful information. If you can install & boot from a USB SSD, then it likely means the internal drive is bad. If you cannot boot to an external macOS SSD, then it doesn't really help since some internal drive failures can affect the ability to boot from an external drive...or it could indicate some other hardware failure.

Use a USB Keyboard for this.

As odd as it sounds, make certain that Caps Lock is not on.

I encountered that issue once in a bright sun-lit room when I could not distinguish that the little LED was illuminated.