Go to Device Manger under "Audio Inputs and Outputs" and see which Audio driver is being used by your BT Headphones. I have BT Headphones that uses Microsoft native audio driver and not my Nvidia HD Audio driver:
If you noticed that all Audio devices that uses my Nvidia GPU HD Audio driver are listed under each Audio devices.
Yet my BT Headphones doesn't show that it is using my GPU audio driver but Windows native Audio driver.
Upload an image of your Device Manager showing the above categories to see which driver your BT Headphones are using.
Also look at Windows Sound Panel to see which Audio driver it is using. In my Sound Panel all Audio devices that use Nvidia HD Audio from my GPU is shown including my Motherboard HD Audio driver Realtek with its Audio devices. Yet my BT Headphones doesn't show neither my Motherboard or Nvidia GPU card audio drivers:
So you first need to find out which Audio driver your BT Headphones are using. I imagine it would be the same as mine which is MS Audio driver from Windows.
NOTE: Since you have a AMD GPU card installed you will show AMD HD Audio driver instead which is installed by your Adrenaline driver installation package.
You can temporarily disable AMD HD Audio to troubleshoot without having to uninstall the entire AMD Driver package from your PC.
It is possible there is some conflict with the AMD HD Audio driver and the Audio driver your BT Headphone uses.