So how does it work in terms of ships you get and how much of a ship sim it is? Can I control operations, manage repairs through engineering, assign crew to stations/departments, etc.?
Basically you get to pick a free ship each time you get a promotion, and you can buy more ships with dilithium.
You do get to choose your ship weapon loadout, which obviously depends on what kind of ship you have. Your abilites actually come from your class and your bridge officers. Each ship has a different configuration of bridge officer slots. You could have 2 tactical stations, 2 engineering stations and a science station, or 3 science and 1 engineering, etc. For each of these stations you choose a bridge officer based on what active abilities and passive buffs they give your ship. You can also choose an away team for ground missions, which doesn't have to be the same as your bridge crew.
You also have duty officers you can assign and send on missions, or equip for passive bonuses. The missions are basically generic starship assignments, like have these officers research this thing, or send these guys to go on a diplomatic mission. If you've ever played Assassin's Creed: Brotherhood, it's basically like the assassination contracts you send the NPC assassins on. You tell them to do a mission, it takes a certain amount of real world time to complete, and when it's done you get a reward and can use them for something else. If you want you can go inside your ship and talk to your officers in order to take these assignments, instead of just doing it through the menus, and when I last played there were a few missions you could only get inside your ship. They may have changed that.
As far as "managing repairs though engineering", all gameplay-relevant repairs happen due to space combat, and are usually just ship "injuries" that give debuffs to your performance. You just cure these with consumable items, though you can assign duty officers to make more of those items.
Not sure if that's enough of a starship sim for you, but there you go.