I’m looking for a bluetooth transmitter/receiver to connect bluetooth headphones to xbox [on hold]

So I recently purchased some airpods and want to also use them with my xbox while playing online games.

I have seen that you can use them with the xbox app using this guide But the app has it’s shortcomings. It has it’s occasional glitches with connectivity, it won’t automatically switch to using the app as the primary voice client when connecting to voice using the xbox, and the ultimate downside is it only provides voice chat so no way to also stream the game sounds as well.

So after seeing this video about connecting them to the ipod classic, they used the Hagibis Bluetooth 5.0 Transmitter Receiver so I decided to purchase them thinking it could do 2 way rx/tx at the same time but unfortunately not. It only does one or the other. At least for this configuration so I’m finding.

In my search I found here that the term is refered to as “full duplex” although I’ve tried many different combinations of searches on amazon for full duplex bluetooth atapters and most seem to be for cars and the ones without full duplex seem to only do either or not both at the same time.

My understanding is that the easiest way to achieve this is using the 3.5mm jack on the controllers which would work if I can find one that does both. The only other option would be possibly some usb type adapter like the ones that the gaming hadsets use but only one I could find was advertised as only for connecting to a PC.

Does anyone have any experience with this? Or know a way I can do this?