Can ToothFairy force the bluetooth device to drop its prior connection in order to connect to it?
Yes, this definitely works for AirPods. I’m not sure whether all devices can do this. If it works for you when connecting via the Bluetooth pane in System Preferences, it should work via ToothFairy, too.
My target here is Magic Keyboard / Trackpad. I’d like to shift their focuses using ToothFairy.
Once connected to one device, those peripherals wont appear in Bluetooth preferences in the other devices. So following your answer, I would assume that ToothFairy wouldn’t manage to connect to them. Is that correct?
Correct. The Magic Keyboard/Trackpad are more limited in that they can only be paired with one Mac at a time. ToothFairy can connect to a device that’s already connected to another Mac/iPhone, but it cannot connect to a device that is unpaired (with the Mac running ToothFairy).