Scroball is a lightweight scrobbler for Last.fm which can track music playback from almost any media player on Android, including:
Google Play Music
And many more...
Tracks played while offline will be cached and submitted when internet access is available
This app makes use of the Notification Access permission to read media playback information directly from the system for any app. This is the only way to read playback state for many apps. No other data is read from the system or stored.
Note: certain manufacturers (including Xiaomi) stop apps from starting automatically by default. If you have issues with scrobbling not starting without the app being open, look for an 'Autostart' section in your phones settings menu. For MIUI this can be found in the Security app -> Permissions -> Autostart.