Odd, i had a test with my controller and see it receiving fine in big picture mode, maybe its specifically switch pro controllers. Do you keep your Input Display open on a second monitor unminimized?
Yup I keep it open on another monitor and it works up until I click into game. I've had issues with the switch pro controller working with emulators where I've had to open them through steam to get the controller to work. Not sure if something in Steam steals the input somehow