Try setting up Steam Input for your controller when it is working wirelessly. Setting steam input to use my theustmaster racing rig wheel allows me to use the buttons on wheel to navigate steam overlays etc and fixed many input issues with games and steam. Using a Shield controller to access all my PC games using a shield TV I've found using Steam Input to configure shield controller for using my steam controller configs is a revelation. That’s it Your controller is now up-to-date. Once it’s done, you’ll see a green tick mark above the controller’s photo. The Xbox Accessories app will now begin downloading and installing the update.

I recommend you spend time trying different controller settings and find what works for you and your controller. Once you’ve read it and followed the instructions, click Continue. Some people are recommending you switch off steam input support for non steam controllers because they do not understand how to configure non steam controllers for best use with steam and steam apps. Doing this will help configure your controller for steam overlays as well as steam apps and desktop mode. If you go to controller settings in big picture ui you can choose to register controller to your steam account so that all your steam controller configs can be applied to other controllers. Valve call this steam client feature Steam Input. Steam client now ships with steam controller configuration software that can be used to configure just about any controller and not just steam controllers. What you are describing is expected behaviour.

Xbox bluetooth controller driver