My mouse (Logitech MX Master) supports Bluetooth. It also supports Logitech' s "Unifying Receiver" and has a button to switch between three different Logitech receivers. I think everyone can guess correctly which of these options just works and always does what you want it to.
To clarify if it's not clear - the button switches between three different receivers, Bluetooth or Logitech unifying receivers. Currently I have 2 BT profiles, and 1 Logitech. The mouse works flawlessly
If it's not obvious, the USB receiver works flawlessly. I occasionally have trouble with Bluetooth not connecting (or randomly disconnecting) with the same mouse, but it mostly works okay.
When I connect my AirPods to my 2015 MBP they don't properly connect unless I open and hover over the speaker icon in the system bar. There's also an issue if I start connection with only the left bud, probably the right bud is the main one?