Toggling Universal control and BTT at the same time can now entail a lot of conflicts, as you can see in the video. Attempts to drag files to iPad always fail. And when you move cursor from Mac to iPad, it couldn't get back from time to time. Also when you move your cursor to iPad and then make some gestures like moving 3 fingers up, both Mac and iPad will respond to the gesture. Many bugs and confilcts about Universal Control together with BTT.
Apple doesn't provide any APIs to work with universal control for third party developers yet, so this can not be fixed (as far as I know). If they become available at any point, BTT will support it.