The concept is simple enough, there’s a daughter-board in the Xbox 360 which hosts the RF module for wireless controller connectivity. Once you extract it from the carcass of the beast ...

[octanechicken] has a possible adapter solution that lets ... [octanechicken] was able to get the Xbox One headset controller to work with older Xbox 360 chat headsets having a male 2.5 mm plug.

However, much like the Xbox 360's 3.5mm adapter, a Bluetooth 5.0 adapter ... the Xbox audio will come through your wireless earbuds. This method will also work for streaming boxes like AppleTV ...