We have more than one car with android auto. There is no way to install PLEX, however, PLEX usually appears on the car touch screen. I say usually, because sometimes it will just vanish and not even be an option.
However, when it is present, there are no options to search by “artist”, “album” or “song”. It only gives three options, something like “recently played”, “recently added” or “playlist”. I don’t remember exactly. Can’t PLEX be added to android auto so that it is fully functional?
I haven’t tried the regular Plex app on Android Auto, but I do use PlexAmp almost daily without issue. Might be worth a try.
I’m fairly certain you are never going to get an actual search though since I’m fairly certain that is not something allowed in Android Auto due to being a driving distraction.
I have PowerAmp on my cell phone. It always works in android auto just fine. You can’t “search” by typing, but you can browse complete lists by artist, album or song. If you browse too long, it adds “safety pauses” to encourage you to look back at the road.
PLEX should offer similar functionality. I have more music on my PLEX server than what I store locally on my phone.