Yes and no. The fighters we do see in Sacrifice of Angels don’t show up again until the finale and that’s really just recycled footage. The fighters themselves are highly suspect as they’re not carrier based but rather fly alongside the other ships matching speed so either the fleet is moving pretty slowly or they’re able to maintain speed.
Trek ships in general don’t seem to have high capacity or rapid launch shuttlebays with two noticeable exceptions: according to the modeler who built the Akira-class, they were meant to have large forward and rear shuttlebays for rapid fighter deployment (which was never seen onscreen). The other one was a 3D modeler who was building the Enterprise D deck by deck did a tour of the Big D’s shuttlebay and it is much larger than what we’ve glimpsed in-show.
Then there’s the final bit which is that none of the other races have had short range starfighters, except for the Romulans and those weren’t seen during the Dominion War, only in Nemesis and we never got the sense of their potential as a swarm.
If I had to take a stab at it I would say Birds of Prey, Hideki Class, Miranda Class all fell in the Destroyer Category (Defiant was called a Destroyer-Escort but packs a lot more omph than those ships) and tried to also fill the spacefighter role and were the screening element of any fleet action. Not many of these ended up surviving.
So no what we really end up with isn’t something that’s Babylon 5 or BSG, it’s which fleet packs the biggest punch, and for that Starfleet scraped the bottom of the barrel by reactivating old units such as Mirandas and Excelsiors that could add firepower but were woefully inadequate, crash launch programs such as the Centaur which used whatever was lying around, weld them together and hope for the best, pump as many Galaxy spaceframes as you could. Akiras, Sabers, Norways, Steamrunners, even Defiants always seemed few and far between, and Sovereigns were…somewhere else.