OK xinput does not work over bluetooth in Windows 7, so that is likely the issue there. I'm not sure what it is actually connecting as then, but that is likely why it is not showing, it could be showing in Windows as some weird peripheral and not a controller at all.
You could try the steps and driver in the below reddit thread, it's not strictly for the xbox one controller, but it gets xinput working over bluetooth on windows 7 with the controller mentioned, so should work with a xbox one controller also. @Charco also had the same issue on Windows 7 with his 8bitdo controller and that driver linked worked for him to get xinput working on Windows 7 over Bluetooth.