I've had this issue since 21.2. Switch controllers I try to connect with Blueman only pair for a second before disconnecting, and later attempts will connect and disconnect several times before shutting off.
if I use bluetoothctl directly, I see the same behavior if I pair and then connect on later controller restarts.
However, if I just connect without pairing with the device removed, it will work while the controller is on, but it follows a similar "on off on off" issue on subsequent controller boots. How do I fix this?