Bluetooth has been around for a few years now, but it gets better and more reliable with every passing version. Bluetooth currently sits at V.5.0 and has never been so common as it is now - but there are still some quirks when using Bluetooth with your Series X/S controller...
The long and short of it is that the controllers don't natively support Bluetooth, which is why when you use an Xbox controller with your PC you need to plug it in or purchase a dongle. This does not mean that such headsets can't be used with your controller, however, it just has a few more steps involved rather than plug and play.
Connecting Your Controller
You will need to buy a Bluetooth transmitter that fits into a 3.5mm Jack/Input; as this is what your controller has. Put it into your controller port and turn it on, making the device discoverable by pressing the Pairing button.
As this isn't designed by Microsoft themselves, there won't be a visual indication of the headset being paired successfully, so pay attention to the lights on your headset or pop the headset on to see if you can hear anything coming through.
Hopefully it should be as simple as that! One thing to note, however, is that the microphone will not work as the transmitter will not be built to detect audio coming in, only audio passing through to your headphones themselves; unless you purchase a headset that is specifically designed for Bluetooth use with Xbox and has been verified as compatible.
Another caveat is that you may experience audio lag as the sound has to go through an additional passthrough in order for it to reach your headset, so in online games where timing is everything, you might find yourself in some situations where audio lag costs you a match.
For general story based games that are not competitive the audio difference will be negligible, and will not affect your gameplay.
Need some more tips? Why not check out how to download Space Jam: A New Legacy Video Game on Xbox?