I feel weird reading this thread because I use a Mac all day, every day, and I have never noticed this problem. I honestly had no idea that this was a big frustration for people, and when I saw this thread I thought "why would I need to prevent Apple Music from opening?"
I can't remember ever being annoyed by the "play" button opening Apple Music - the worst it might do is start playing the YouTube video in an open browser tab when I wanted it to play Spotify (it depends on which app i most recently alt-tabbed from), but that's only a minor annoyance.
Am I the weird one? My system rarely starts up because I rarely turn it off; why bother? (`uptime` reports that the last time I restarted the computer was 79 days ago.) And I pretty much always have Spotify or YouTube (the two main places I open in the background, so Macos doesn't need to open a new app to start playing.
What am I doing right?