When I tried launching Battletoads on PC game pass it would only let me control it with mouse and keyboard. I tried connecting my Xbox One controller via a wireless adapter, and via USB, but neither would work. However, when I got to the character select screen I found that pressing start on the Xbox controller would add a second player that I could control via the controller.
I figured out the cause of the problem, and wanted to share it here. Apparently the game doesn’t like it if you have a flight stick plugged in (as many probably do if they’ve been playing Flight Simulator 2020). As soon as I unplugged it and launched Battletoads again it recognized the controller input for player one without any issues.
Hope this helps you if you’ve been frustrated like me.