Based on everything you've described, your assumptions seem sound. If the Magic Trackpad connects to the Mac mini and the mini is discoverable by other devices, then Bluetooth on the Mac mini itself is clearly functional. Since your keyboard is also visible to other Apple devices, the issue is pretty clearly narrowed down to a pairing or caching issue between just that keyboard and the Mac mini.
As such, I suggest that you try the following:
Manually Reset the Keyboard
- Turn off the keyboard by holding the power button until the green LED goes off.
- Forget the keyboard on all nearby devices it might have paired with—especially your iPad and MacBook Pro. Sometimes Bluetooth pairing conflicts cause devices to refuse to show up properly.
- On your Mac mini, open System Settings > Bluetooth, and remove any existing instance of the keyboard if it shows up at all.
- Now, hold the power button down on the keyboard and do not let go—you want to keep it in discoverable mode.
- While still holding, go back to the Bluetooth menu on the Mac mini and see if it pops up.
- Once it appears, try pairing it while continuing to hold the power button. Only release the button once the pairing is confirmed.
Reset Bluetooth Module on the Mac Mini
- Open Terminal and run: sudo pkill bluetoothd
- Alternatively, hold Shift + Option, click the Bluetooth icon in the menu bar (if visible), and choose Reset the Bluetooth module (this option was removed in Monterey+, but some still see it depending on the build).
