Thanks for the nice review! The behavior you're describing is almost always a Firefox/Android permissions issue rather than the add-on itself.

Try changing these settings if they are available:
1. In Firefox → Site Settings, set "Autoplay" option to "Allow audio and video."
2. Long-press the Firefox app icon → App Info, and ensure Firefox has the "Music and audio" permission.
3. If you have a system or third party lock screen media player, make sure any autoplay settings are enabled.

These options should allow playing in the background without needing to reopen the browser or manually trigger playback.