I legit can't connect a Bluetooth pro switch controller without it freaking out and pressing the jump button non-stop lol
I'm assuming you're connecting the controller before you run the game (doing it while running can get wonky, apparently).
Unity is weird with bluetooth controllers on PC and I know Nintendo ones seem to need a special wrapper to do anything with. If you're on Windows, there's x360ce, a utility that translates everything into Xbox 360 input which should get you more consistent results.