I have two of these. Both are on the Bluetooth firmware and honestly? They are really nice controllers. They also work wired, but can be put in pairing mode by holding down Y and the Stadia button until the light flashes orange. The weirdest feature is "tandem mode," which you activate by plugging *another controller* into the USB C port on the Stadia controller. Now both controllers will act as the *same* controller, so no two player action, unfortunately. But it has been confirmed to work with all of the following:
- Xbox 360 wired controller 
- Xbox 360 wireless adapter with a controller connected
- Xbox One controller 
- Xbox Series X/S controller 
- Xbox One Elite Series 1 and 2 controllers
- PlayStation 3, both Dualshock and Sixaxis controllers
- PlayStation 4 Dualshock controller 
- PlayStation 5 Dualsense controller 
- PlayStation 5 Dualsense Edge controller
- Nintendo Switch Pro Controller
- Amazon Luna Controller
- Another Stadia controller

This means you can use a Stadia controller as a Bluetooth adapter, which [Bringus Studios](https://youtube.com/@bringusstudios) did in [this video](https://youtu.be/3l3e68b90dw). While you're there, check out his channel, he does some cool stuff!