When it began shipping last year, the Stadia Controller worked wirelessly on TVs hooked up to a Chromecast Ultra, but using it with any phone or laptop required it to be connected via USB-C cable, which doesn't make for the most comfortable gaming experience. Earlier this year, Google rolled out the ability to connect wirelessly via the Chrome browser, and starting today, users can now do it with any supported Android device as well.
Once the ability goes live for you, you'll need to make sure your phone and Stadia Controller are on the same Wi-Fi network, then launch a game and follow the pairing instructions that appear on screen. Even with the latest APK file from APK Mirror, it doesn't seem like wireless pairing is working for us yet, though your mileage may vary.
Stadia's momentum has been hampered by a lack of features like iOS support and Google Assistant integration (although that seems like it's getting a little closer now). If Google can keep on adding features that arguably should've been there from the start, it'll do a lot to reassure game developers and players alike that Stadia is here to stay. And hey, the Stadia Controller happens to be on sale now!