What to do after finishing the story campaign?

If you're really only interested in stories, then the game ends with Resurrection for you.

As you've stated, this is mainly a multiplayer game. Galactic Assault and Starfighter Assault maps have some "backstory lore" behind them (e.g. the Death Star II map is about a crashed Rebel ship's survivors trying to flee from the station), but these are just there to provide some context and atmosphere - it's nothing compared to what you're looking for.