Since XInput superceded DirectInput, it's been hard to develop a Windows game with support for anything other than XBox-style pads, unless the developer physically owns all the different pad types they want to support and has time to individually QA them. Major publishers can budget for this, but not the smaller teams that mostly publish on itch.io.
In the case of a game like Celeste that doesn't really need analog inputs for anything, you might have more luck using keyboard-mapping software for the pad and then letting the game think you're still using the keyboard, instead of trying to get the game to notice the gamepad directly.