Make sure you have your controller handy. After pressing the connect button on the Xbox, you need to do the next step within 20 seconds. Press and hold the sync button on your controller.
Xbox Elite Controller Series 2 gamepads are notoriously issue-prone, particularly with the bumpers. Thankfully, fixing them ...
Only some Xbox controllers support Bluetooth ... On the Switch Pro Controller, for example, you have to press and hold the sync button next to the USB-C port.