The issue to me is that there is not a full Xbox Series X controller driver for bluetooth. That means everything after that will be a rigged system that does not have the same level of support. The whole thing is a bit of a bait and switch then, as the bluetooth is not fully supported.
The only reason I bought the controller was to get full windows integration on every app. If that only works with the wireless dongle they sell...then I wouldn't have bought the thing. It sounds like right now that is the case.
So does it work on bluetooth...the answer is sort of. That means it shouldn't be listed as supporting it. It is a downgraded support from cabled connection and at this time that is just nuts.
Right now I cannot sit 2 feet away from my bluetooth and play the same way I can cabled. I have to jump through hoops and deal with all sorts of configuration issues....which is exactly what people using this controller rather than a generic are trying to avoid.
Give us a full xbox series x controller driver on bluetooth, or remove the labeling that says the series x controller supports bluetooth. It doesn't. It supports a generic emulation using a substandard driver.