So some of the abilities it is pretty easy to see how they work.
Logistics speeds the loading and unloading of ships. And if you put an officer in a logistics slot in a task force, they train up to >50% in about 10 years or so, so between the fleet command bonus and the ship captain, you can get a 100% increase in loading speed for not much investment.
Fighter bonus increases the accuracy of fighter beam weapons, and if you build a bunch of cost 1 BP 'fighter' PDCs and park your fighter bonus officers there, they tend to train that up. RP-wise, I am reminded that the Japanese started WWII with a very experienced and well trained fighter pilot force, but because they flew very fragile planes, they tended to lose their pilots over the course of the war, resulting in them having much lower average pilot quality towards the end of the war. In part because they were so hard pressed they couldn't cycle experienced pilots back to train new ones.
So if you spend 10 years training up a bunch of high quality fighter combat bonus officers, if you LOSE them, suddenly your whole fighter force is a lot less effective, because it takes so long to train up good new officers.
Fighter OPs supposedly was supposed to improve fighter reload time, but I have heard that it is borked and actually increases the time it takes a hangar to reload fighters.
Now, if the task force commander has a mining bonus, do asteroid mining modules get a boost too? Or sorium harvesters if the TF commander has a factory bonus? I am also trying to figure out if asteroid mining modules are better or worse than automated mines. The asteroid mining modules take less space to ship, and benefit from naval mining officers, but the economics of it seem to depend on how far you have to ship them.
What exactly do operations, intelligence, and communications boost? Is it worth putting early officers into a dummy task force to train them up?