It was a behavior I found myself idly expecting from a miniplayer, not sure from whence, and sad it didn't work.
I think this should be pretty straightforward with the "modern" method since you should be able to grab the AppUserModelId (though that may need to be exposed from the dll also, as currently the "Player" display shows "MediaPlayerDLL")
I may come tackle this with a PR myself, but wanted to throw it out in case y'all were already thinking about it