Other people have suggested that the app being set to not go to sleep will fix this issue. It does not for me. What happen is shortly after the screen goes off the music stops only when using Bluetooth. When you wake the phone it starts back up. For myself and my wife (both S10 users with spotify premium listening to downloaded lists) spotify was not set to go to sleep in settings. It seems to happen less when power saving mode is off but happen with both settings. The only thing that seems to "fix it" is to have wifi off and power saving mode off.... But nonetheless I have had it happen multiple time with both off - just less often.
What I've done so far -
*uninstall and reinstall spotify
*check power saving mode to make sure spotify isn't going to sleep.
*checked settings within spotify for anything I might be missing.
Have you checked the battery optimization setting for Spotify?