I do not remember which models I read about that did that and never owned a gameport joystick/gamepad with extra buttons. MIDI was (de-facto) standard gameport pins and using the UART wired to the MIDI input pin was probably more convenient than to read serial signals from the buttons but I do not know how common it was to use that pin instead of the button pins.
Found this page that has a list of some 10 different protocols for sending digital signals from joysticks to a gameport:
https://dosdays.co.uk/topics/joysticks.php
Other than the sidewinder and GriP protocols I have not managed to find any specs for the other protocols. I clearly think I remember from back in the day that using MIDI for extra buttons was a thing so it may be one of those other protocols did, or it could be that I am just wrong.
https://retrocomputing.stackexchange.com/questions/24946/how...