You cannot connect AirPods directly to an Xbox for game audio
Xbox consoles do not support Bluetooth audio for headphones like AirPods
Use the Xbox app on a phone or tablet for party chat with AirPods
Use a Bluetooth transmitter plugged into the Xbox controller or console
Connect the AirPods to the Bluetooth transmitter
Use the Xbox mobile app with AirPods for voice chat
Use the TV or monitor audio for game sound
Use a wired headset with the Xbox controller for direct audio support