I am on Unity 2022.3.28f1 with Input System 1.8.2
I am literally working through the same issue and came across your post. While Googling, I came across this post as well of a person who is taking a bit of a bet to remove the XInputDevice when it is detected within a tiny timeframe of the Switch Controller detected. I am running out of other ideas and that seems like the only decent solution for now so I think I will go with that and hope it works. It’s not the best as it does make a bit of an assumption but it could work.
I even tried making a Control Scheme separate from the Gamepad scheme I have for the Nintendo Switch Pro Controller. That did not help. Looking at the Input Debugger I see the exact issue you see. If you right click on XInputControllerWindows and remove it your device will work as you expect which is what the code I linked does.
I imagine this is in part due to Nintendo software and how it interfaces with our computers and it likely being a bit of a black box due to poor documentation. I also imagine Unity devs working on the Input System have to do a fair bit of reverse engineering to get a lot of these controllers to work.