Have you tried Bridge Commander or the not actually star trek, but still totally star trek game Artemis?
They’re basically that. Randomly generated scenarios where you, and a few friends, command a Starfleet vessel to solve dilemmas or just exist in the world. The fun is mostly in the MP aspect (though Bridge Commander can be played solo), and the missions are pretty samey and mostly explained through text briefings. But it really feels like being on the bridge of the Enterprise.