I'm having the same issue unfortunately, with the PS4 Controller through DS4Windows. Better than the Switch controller though, which seemingly inputs every button simultaneously so Toree just immediately jumps off a cliff as the level starts.
I definitely appreciate it existing though! It's a really nice tribute! I'm also just hoping I'll be able to play it at some point. 😅
Try playing around with different camera re-mappings. Unity's input manager often mistakenly maps camera to shoulder triggers instead of right analog stick for PS4 controllers.
As for the Switch controller problem, I use Betterjoy and follow these instructions: https://github.com/Davidobot/BetterJoy/wiki/HIDGuardian-and-Steam-(Big-Picture)