The Federation is post capitalism but only by leaning very heavily into hierarchy. I would argue that isn't really post capitalist at all but just a variant similar to communism.
The means of production in the Federation is still well removed from the people. The writers even fooled once with replicator credits. Their military has no hint of democracy and captains or in this case school presidents have enormous authoritarian power.
Furthermore the plot of Academy leans heavily into corporate managerial fantasy by giving leaders cool ways to "teach" teamwork etc.
From a leftist point of view Star Trek remains unapologetic copaganda most of the time. Even DS9 is a show about a "good" military base.