>Is the combat turn-based, real-time strategy, or something else?

Real-time tactical. You personally pilot one ship (accel, decel, rotate ship, slow strafe while pivoting) and can pause whenever you want to give orders to the rest of your fleet, including ordering ships to retreat and calling in undeployed reinforcements depending on your deploy limit. The AI is actually pretty good and the orders are robust in terms of telling units to go after capture points, search and destroy, escort a target, and so on. You are notionally limited by 'command points' so you can only give orders so often but I never personally found it limiting, since once you give one order, you have a time window where all subsequent orders are free.

You can also choose to switch which ship you're personally commanding at any time, with a minor delay as your personal drop pod needs to actually jet across space to the other ship. Useful if your ship gets shot out from under you or a ship is under trouble on the far side of the battlefield and you don't think you can give other commands to bail it out.