That's an option that in my opinion would be really useful both in the new music player and also in the background music feature.
When I'm for example watching a video on youtube and when I finish watching the video I keep opera gx open when opening a game, I usually don't want to hear my Spotify playlists or the background music of opera gx because they don't match the game most of the time and the games most of the time have a music of their own.
So I think it would be really cool to add an option in the settings of both of the music players- the background music and the music player- that the music will be muted when opening a full screen app or maybe even only when switching to another app. (For example the Microsoft store)