I will say, even with my updated BT/WiFi card, I too am getting some weird issues with that in Monterey.
For example, sometimes when I switch to Windows (reboot, choose windows @ OC boot picker), my BT mac Keyboard has a hard time connecting, so i'll have to use Windows on-screen keyboard to log in, and then remove and re-add my mac keyboard.
Then when I reboot to switch back to mac, although the keyboard works fine in the OC boot picker, as soon as the apple logo is done loading and Monterey login screen appears, my KB won't connect, and I just sit there until the "bluetooth assistant" shows up, it says it's pairing, but it just keeps spinning and spinning and spinning until I manually reboot.
Not sure what gives here, but I am thinking about reflashing my bootROM with a deep nvram reset just to see if that helps with anything.