sorry, overlooked your message before posting my “problem solved” (or rather: “problem silently went away”) message. the cold start seems to have removed some deadlock in the machine.
regarding the bluetoothctl command: if I do this now (after it in fact works and the bluetooth mouse is connected), I get a sensibly message (namely agent regestered and prompt for the connected (single) device (the mouse).
I will remember this command and the possibility to use it for handling bluetooth connections from the CLI (thank you :)).