If you're running a non-iTunes music app (including web pages, on newer versions of macOS), the play/pause button goes to whichever one last grabbed the audio. So if you start VLC (or whatever) first thing (or add it to the auto-start items), then the play/pause button will always go there.

It always worked as a pause/play for already playing media, my complaint was about its use as a launcher. Made muscle memory tricky as its behaviour depended on what was running at the time.

There's a great little utility called BetterTouchTool that will customize the default play button app. It can do a bunch of other little things, too. https://folivora.ai

You can use software like this to customize media keys: http://beardedspice.github.io/

I believe it’s just in System Preferences -> Keyboard, but may be mistaken.

I had a another look in "Keyboard Shortcuts". Lots of shortcuts, including a category called 'App shortcuts'. No mention of iTunes / Apple Music. I think it's just hard-coded in the OS.