That is maybe questionable behaviour from the headphones. But the worse problem is that there is no way to change what media player is used. I don't use Apple Music, have no songs in it and no subscription. But it opens that rather than the player I do use.

I'm pretty sure I have also launched Apple Music accidentally with some keyboard button or touchbar action. For a "premium" device having to close Apple Music (effectively an ad) a few times a week is not acceptable.