Xbox one x bluetooth headphones?

I would also like to use the Xbox for streaming, I have already found the right webcam and a microphone for it, everything fits.
But now I'm desperate on the headphones. I want to use it wirelessly, since the Xbox (for whatever reason) does not support Bluetooth, I probably need an adapter. But I would not like to connect anything to my controller.

I would also like to have "headphones", no headset, so without a microphone. It would also suit me as a compromise if you just don't see the microphone, retractable or something.

I really don't find anything on the Internet. Can someone please help me and recommend something?

I give the perfect headset for you

all current Razer models can retract the mic

(The octopus ultimate

Form the nari in three depending on how expensive it should be)

the best would be the xbox verified Razer headsets

The Thresher Ultimate

https://www.razer.com/eu-en/gaming-audio/razer-thresher-ultimate-for-xbox-one

The Thresher TE

https://www.razer.com/eu-en/gaming-audio/razer-thresher-tournament-edition

The Thresher

https://www.razer.com/gaming-audio/razer-thresher-for-xbox-one

and finally the Nari Ultimate for Xbox

https://www.razer.com/eu-en/gaming-audio/razer-nari-ultimate-for-xbox-one