Why is Google Play Music the only app that produces a "Browse" button on my car stereo?
This &quot;browse&quot; feature is probably part of &quot;Audio/Video Remote Control Profile&quot; aka AVRCP. AVRCP has different versions with different feature sets. Browsing of playlists was introduced in version AVRCP 1.4 and improved in version 1.5, according to wikipedia.
This bluetooth profile must be supported (in the correct version) by the the car stereo, the mobile phone as well as the app.