Based on the experience that I think is trying to be catered to. There should be some options in the settings around how the background music behaves.
Currently when a video is played on YouTube for example, the music will immediately mute and the video audio will play. But I think the experience can be improved if the music quickly faded out. It could be very quick too, less than half a second would give a good feeling of transition.
However, it could be taken a step further by also allowing the user to modify the fadeout timing themselves in the setting menu.