Assuming 400 is at the higher end of starship crew sizes, the station as imagined by Mandel ought to suffice for processing up to half a dozen at a time. That is, there'd in that worst-case scenario be something like 1,200 people (half the crews) rummaging through the services and entertainment opportunities - and each of the three "little sombreroes" as depicted seems capable of accommodating 400 people in the sort of conditions a lower middle class hotel would offer today, with some 100 reasonably sized staterooms per sombrero.
That the station had to specifically summon Kirk's ship to deal with the Klingons, rather than just enlist the services of the starship currently foraging at K-7, suggests that starship visits aren't quite that
frequent after all. Thus, 300 staterooms, for people for whom anything better than bunk accommodation is likely to be an upgrade, should suffice. Mostly, visiting crews would not be spending their station hours in those staterooms anyway: those might be reserved mainly for non-commercial mingling and prostitution purposes, private business negotiations, and the occasional murder mystery.
The small craft hangar is the part that looks a tad small in Mandel's take, mainly because one would expect lots of support systems in addition to the empty hangar itself. Starship docking would be facilitated by the outspread nature of the little sombreroes, with docking ports potentially hidden inside the top domes (and matching the bottom domes of common Starfleet vessel types?).
Why is illumination indicative of deep space? Wouldn't we rather think that there is a star nearby to provide it? It's not as if we see signs of self-illumination with floodlights or the like - save for the pennants of Kirk's ship in the DS9 version, rather tastefully done so as not to contradict the lack thereof in the TOS version.