By the way, why would there be a brig there when even the ore ships call there only once every 20 years?
Well, it is (in) what the signage specifies as "RESTRICTED AREA". Kirk speaks of monitoring Gary from the "dispensary screen". We might argue that a place that has such extensive medical facilities that there exists a special "dispensary" would also have a quarantine room, which we would be seeing here.
Or a kitchen, a sauna, and a proper brig, for that matter. So interestingly, it's actually a wider issue than it seems at first, and the refinery indeed appears to cater for crewed operations.
Unless we assume Kirk wanted Mitchell to be monitored from the screen at Dr Piper's dispensary aboard the starship... Which makes some sense, at least tactically, but it's odd that this specific starshipboard screen would be used when Kirk's security department no doubt would have many screens available aboard the ship, too. (And no, "dispensary" isn't the name of Dr Piper's overall workplace in this episode - it's called "sickbay" just like in the other episodes.)
OTOH, if ships come all this way to the very edge of the galaxy, perhaps they want to spend a month or two recuperating before a return journey, and these facilities are absolutely needed for this reason. Which reminds me of another question: why is the place visited by "ore" ships?
I mean, ore is dead weight with tiny bits of useful stuff within it. Why should anybody haul ore either to this facility, or from it? Shouldn't the facility remove all the dead weight and allow just the useful stuff to be shipped?
If ships bring in ore which then gets refined, why do they bother to come all this way to the middle of nowhere? If ships just haul away ore that gets refined where civilization is, why does the distant mining site have this vast "automated dilithium cracking station" there?
Oh, well. In any case, I do dig the eyes. Especially as they don't glow or change color or otherwise draw more attention to themselves. They look surprisingly "real" for that reason...