Hey mate, could you try something for me.
I'm adding a page to rebind your keys to hopefully make generic controllers work as well.
Sadly I threw my previous playstation Knock-off controller away a while back so I couldn't check to see if it works.
https://yannick-h.nl/Projects/rebind/index.html
This is a unity webGL build with just a keyrebinding example so would you mind just opening it and seeing if your controller gets recognized when you try to rebind the gamepad (or maybe keyboard) controls.