Bug Impossible to use wired Switch controller with Unity New Input System

Hello,

I've already seen some people complain about this but I never found any solution.
Unity detect all my controllers (PS4, Xbox and Switch with a message in the console) but when I hit play or if I try to listen, the switch controller doesn't react at all.

I found a way around by uploading my game to Steam (I guess they have something to make all controllers react the same). But now I want to build a demo for my game as a downloadable executable on itch.io and I won't have the Steam system inplace so.

What should I say to my players, is it something Unity related ? Or can it be fixed by downloading a compatibility software?

I'm using Unity 2021.3.0f1 LTS and I have the latest version of Unity Input Packaged installed
Thank you!