I have two other plex clients active on the network right now: an Apple TV that is playing music and a web client that is controlling the music (a third iOS client is occasionally open to control the music, but not consistently). Yet, the Player menu item shows only Local as an option.
Hard to say exactly what the issue is without seeing some logs (Application.log or Server.log should both show it trying to connect to available players).
One tip: You can (re)select Local to force it to kick off a discovery/testing of players and servers.
iOS specifically can’t run forever in the background, so usually you have to start it up, and then refresh the players inside Plexamp to get it to show up. The tvOS app should be able to live on the TV screen for longer, of course.
