Great news … you can use your Stadia controller wirelessly on your PC.
Taken from TPU … The Google Stadia controller launched alongside Google Stadia 6 months ago and was touted as the controller for all platforms with integrated ultra-low latency features. However, PC users could not take advantage of the ultra-low latency features which connects the Stadia controller directly to your Wi-Fi router. PC users have instead had to connect their controller to their PC with a USB Type-C cable. Some users report that this will increase compatibility on obscure systems by offloading the input handling to Stadia’s servers.
“Starting this week, you can now use the Stadia Controller to play wirelessly on your laptop and desktop. You no longer need to connect your Stadia Controller physically to your computer to play your favorite games. You’ll be able to link your Stadia Controller and Stadia.com through your Wi-Fi network and play without a USB-C cable connection.”