Yes I was referring to the updated controller they started shipping when the Xbox One S was released, I'm pretty sure that's the only one they have been making afterwards until the Series X was introduced?

These controllers use some kind of DRM that requires disabling a feature of the BT stack (ertm) using a non-persistent kernel parameter that breaks other BT devices. I

The fact that they mentions doing nasty hacks to the BT stack implies that it's BT they are using and hence the S controller because you yourself stated it's the one that supports it.