I would expect full campaign mode to involve something more like an RPG mode between missions. The player would move through the ship, interacting with other pilots, playing card games in the pilots' ready room, trying to pick up deck hands at the bar, receiving briefings, and perhaps even finding traitors among the crew.
I'd also expect some micro-transactions (since that's more of a thing nowadays) giving you decals for your fighter, maybe requesting specific mechanics to maintain your ship, and once you get to wing-leader status, being able to recruit specific pilots to fly with you.