If you have BigSur 11.1 and are having issues here are three solutions that have helped other users.
Solution 1: Reset Bluetooth on the Mac
If you are having problems like you can initiate the connection from the Phone/iPad/Apple TV but the KeyPad window does not show, you can reset the bluetooth connection.
https://macpaw.com/how-to/fix-macos-big-sur-problems#bluetooth-not-working-big-sur
- Press Shift + Option and click on the Bluetooth icon in the Menubar
- Click on the option “Reset the bluetooth module”
Go to preferences in KeyPad and Click “Launch Bluetooth Settings…”, this will make KeyPad discoverable. Now connect to the Mac from the Phone/iPad/Apple TV/Android Phone.
Solution 2: Clear connection between Mac and Device
If you are having problems like you can connect and use the Keyboard, but are not able to use the Mouse/Media keys.
- Forget the Mac from the device bluetooth settings (and the device from the Mac)
- Delete the connection to your device in KeyPad Preferences
- Reboot both the Mac and your device
- Connect using KeyPad again.
This is a brute force solution that has worked for a lot of users. The issue is related to the bluetooth implementation in the Mac but I have not been able to get clear repeatable steps so that I can report to Apple.