With the Shield, the Plex Media Server and Plex client are both updated via the Google Play Store. They are separate apps and are updated independently of each other.
If the Google Play Store is set to update installed apps automatically, then both should auto-update. If not, you can manually update the apps.
1.23.2.4625 was released in June.
Updating to the current version, 1.24.5.5173, won’t help with remote streaming options. You will pick up some bug fixes. You can see the details in the release notes.
