Do I understand it correctly, that one has 7.1 Surround by headset only with adapter or sound card and it is with the Xbox no Sorround 7.1 sound?
Ergo 7.1 is only on the computer or how?
For a 7.1 surround sound, for example, the sound card in the PC requires the function. For light cable, I think it remains at 2.1.
This only works with headsets if there's a built-in sound chip built in, so the sound card plays no role in the PC.
Of course you can also reach 7.1 via adapter. But what do you need a 7.1 sound system for (I know you did not mention it)? 5.1 is quite enough
With the XBox I think only 5.1 via HDMI is possible, just as with a Playstation 4.