A real military I imagine would always be using cruiser or larger sized carriers in fleets utilizing fighters or bombers. On that note, I absolutely believe there is a place in-game for additional cruiser and capital sized carriers. Maybe something a little less extreme than the Astral in the capital class, and something a little slower and heavier in the cruiser class.
See "escort carrier" or "light carrier." The real world escort and light carriers may be more in line with the cruisers of the time than the destroyers and the real world fleet carriers may be more in line with the battleships of the time as far as sizes go, but in Starsector we can infer from the Heron and the Astral that the standard fleet carrier is a cruiser-scale vessel rather than a capital-scale vessel - or at least that if it is capital-scale, it's a small capital ship. What the navy would be building in peacetime is another question, as is whether or not there would be a dedicated design when converting the Tarsus or using the Gemini is adequate - though I still feel that the Gemini is more accurately described as a purpose-built escort carrier rather than a freighter conversion.
Also, the US Navy, a real military organization, built more escort and light carriers during the Second World War than full-scale fleet carriers. If Wikipedia's numbers are accurate, of the 151 carriers in service with the US Navy in the Second World War, 122 were escort carriers, and at least 50 of those were purpose-built escort carriers rather than conversions. It's true that real-world escort and light fleet carriers are about the same size as real-world cruisers of the same era, but then, real-world full-scale fleet carriers are roughly the same size as the battleships of the same era, and the supercarriers are even larger; in Starsector, this is not the case, and it is the supercarriers that are about the same size as the battleships and the full-scale fleet carriers which are about the same size as the cruisers.
The Gemini and Condor fill the destroyer sized carrier niche quite well. Really, I don't think there's any reason a "dedicated military" destroyer sized carrier should exist. From an in-universe standpoint, there is no point. Fighters and carriers are inherently large-fleet craft, and military fleets with their massive budgets and R&D resources are always going to prefer a larger, more capable, more survivable carrier. The whole destroyer sized carrier concept is very neat, but conversions fit this role ideally. It's the whole "some civilian decided he wanted carrier capability but couldn't finance a full scale option, so this workaround is available". Alternatively "fighters and strike craft are becoming a part of military doctrine, and new cruiser or capital options take time to develop, so in the mean time here is this inexpensive standby".
I agree that the Gemini and the Condor fill the destroyer-scale carrier niche reasonably well. I disagree that this means that there is no reason why there should not be whatever you mean by a "dedicated military" destroyer-scale carrier (presumably, one designed from day one to be a light or escort carrier, though in my opinion the Gemini already is this despite its description), though I also don't feel that there must be another light carrier introduced into the game. The rationale for including another light carrier really depends on how you think that Starsector's convoy escort and support details would be handled by a space navy charged with taking care of things. There is a clear trend away from guns in favor of energy weapons as you progress from low-tech to high-tech ships, which leaves a conspicuous lack of late-midline or high-tech light carriers. It's not necessarily a hole that needs to be filled, though, as if late midline and high-tech designs are peacetime designs, there's a decent chance that design priority was given to the big ships that are difficult to produce quickly, rather than placing emphasis on smaller ships that are easier to build quickly - though this doesn't help explain the relative abundance of high-tech frigates.
