According to the latest announcement made by Valve, Steam Client Beta added support for the Nintendo Switch Pro Controller.
The Steam Controller team thinks that Nintendo Switch Pro Controller is a great device with a feature set that pairs nicely with your Steam catalog. The d-pad is ideal for fighting games and platformers and the gyro enhances aim in your action/FPS titles.
If you want to try the Nintendo Switch Pro Controller on Steam, you need to go and check Nintendo Switch Configuration Support option in the Controller Settings page. You can visit here and follow the steps in order to enjoy your Switch controller.