If you want the app for nostalgia or to use it strictly as a local offline media player, you can find the final stable versions (8.29.x) on reputable third-party repositories.
Google Play Music was officially discontinued in late 2020 and replaced by YouTube Music. While you can still find on various archive sites, the app's online streaming and cloud storage services are no longer functional. How to Download the Google Music Player APK google music player apk download