Seems like your links answer the question: it's up to the app playing music, and there are some suggestions of apps that let you choose.
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I was always the guy who made custom notification sounds for every app, going back to the flip phone days. Until I got a Pebble watch back in 2016 and permanently put everything on vibrate-only.
Last year, I went back to a regular watch and turned on the notification sounds again...
Anyway, I turned them all off a few days ago for some reason, and just haven't cared to turn any of them back on. It's been really nice. I think I'm going to just set a notification for phone calls, and texts from my wife.
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