If you want to add depth to Carrier Fighter handling then the obvious way to do it IMHO is to open up hangar design choices based on realistic restrictions for Carrier Operations.
This means that either through alot of design parameters (when designing hangars), or through separate modules that can be designed you would add capabilities that assist with the fighter turnaround. This is done in combination with reducing the size penalty on Hangars which is currently "abstracted" to facilitate such things.
I'm talking about things like:
- Launching speed, how many Fighters that can be launched per minute ( could also have tradeoff of module size vs cooldown similar to missile launchers if done as a separate module ).
- Recovery speed, how many Fighters that can be landed per minute
- Refueling speed, how many Fighters that can be simultaneously refueled and what speed it's done at
- Rearming speed, how many Fighters that can be simultaneously rearmed and what speed it's done at
- Repairing speed, how many Fighters that can be simultaneously repaired and what speed it's done at
- Maximum size of fighters that can be handled by all the above
( if done as separate modules some kind of "free" baseline that permits very slow operations would be needed for ships with a single parasite or small utility hangars where adding all the modules to manage operations would just be messy and don't add fun gameplay )
- Armor/Damage control ( If done by designing hangars ) could add interesting depth to prevent parasites and munitions on them going boom in secondary explosions.
The goal of this would be to allow you to tailor Carriers for alot of different roles like Jump assaults ( that can launch loads of fighters super fast ), for long range standoff ( slower turnaround ), for defense (launching anti missile fighters fast) or maybe just for logistics/transportation with minimal turnaround. You could also tailor Carriers based on what kind of fighters they are meant to operate which can have design and operational impact.
Much of the tools to do this might already be mostly present given the rework to ship rearm/refuel that has been done, but it would still probably be quite a complex undertaking.