I still haven't figured it out.
Maybe it only works with a wire.
Gonna check it out over the weekend.
But if it doesn't show up it might be due to Xpad driver since I believe it mimics regular Xbox controller, and that one doesn't have any mic or input jack.
Maybe it will work with a different driver then like XpadNeo there are a bunch of them and on CachyOS they work as DKMS (Dynamic Kernel Module Support) the only thing is that they disable Xpad.
Linux driver for the Xbox One wireless dongle. Contribute to medusalix/xow development by creating an account on GitHub.
github.com
Xow lists working jacks and Elite 2 controllers. I would have to dive in into this subject and see if it will work with non MS controllers. But it specifically reference MS dongle so I suspect it doesn't.
EDIT: There was this Xpad driver on github patched almost weekly and I can't seem to find it on mobile.
Maybe I have it on my PC in bookmarks.