Google notes that you have until December 31st, 2023 to update your gamepad. To connect the gamepad to your PC with BLE, the computer will need a compatible adapter. Here’s the whole procedure as described by Google: What you’ll need:

A Stadia Controller A computer with Google Chrome version 108 or later A USB cable

To enable Bluetooth mode: Tip: If you have a Linux computer, you might need to add new udev rules before you can use or update your controller. After you enable Bluetooth mode on your Stadia Controller, you can connect it to a device, like a computer or mobile phone.

Note: If the status light doesn’t pulse orange, hold the Stadia button  and  simultaneously for 2 seconds.

After your Stadia Controller connects wirelessly to a device, its status light will turn solid white.