Ok, the report does not indicate you have anything installed that should be interfering with Apple Music causing it to quit playing.
Is your Music Library being stored on an external drive? If that is the case I wonder if the drive goes to sleep after a period of time where Apple Music will then stop playing.
Does it seem like it happens at a specific time like it may be Sleep related? I tested on my Mac and the Music continues to play after the screen saver appears and also when the screen went black, but if I manually put the computer to Sleep by going to > Sleep, then the music is paused.
For further testing, there are 2 steps that I would take to see if it makes a difference.
- Create a New User and see if the same thing happens on that users account.
Add User to Mac
- Start up in Safe Mode and see if the same thing happens. After checking, just restart again normally to exit Safe Mode.
Startup Mac in Safe Mode