Touch ID on Magic Keyboard Not Working; Logitech Issue?

I just received a Macbook Pro 16" (M3 Pro) for work, and I bought a Magic Keyboard with Touch ID. When I try to enter my fingerprint, it doesn't recognize it at all. I click on "Add Fingerprint" and the screen comes up, but putting my finger on the sensor on the keyboard does nothing. I have a fingerprint recognized on the Macbook itself, and that works fine. I tried connecting it via USB, I tried it over Bluetooth. I tried turning it off and on again. I tried restarting the Mac. Nothing works.

One other thing I noticed is that the moment I first plugged in the USB dongle for my Logitech MX Ergo mouse, it tried to recognize it as a keyboard. Also, when I click the "Change Keyboard Type" button in Keyboard settings, it brings up a screen called "Keyboard Setup Assistance" and says "Your Logitech device cannot be identified and will not be usable until it is identified." But when I go through those steps, it doesn't make any difference.