Google emailed to tell me that I had "spent time building my Google Play Music library", which was news to me since I've never used Google Play Music.

This article gives some options, and mentions using Google Takeout to download music you bought. If you're a subscriber and don't own the music you can only play it though one of their services, of course.

To play music or videos on Android I use VLC - which is pretty basic but is free, open-source, and doesn't nag me or try to sell me anything. You could try that. But there must be plenty of other players for Android.