So, let's take the actual in-game text:
"Built to the specifications of the 14th Domain Battlegroup which founded the Hegemony, this vessel is a prime example of the Domain Navy's 'decisive battle' doctrine, particularly exhibited by a series of radical structural modifications performed using pre-Collapse industrial technology."
First and foremost, it does not necessarily imply that the XIV Battlegroup ships we see in-game are from the 14th Battlegroup itself. What we know is that a lot of XIV Battlegroup materiel - described as irreplaceable - was destroyed in the First AI War, let alone the second. But I'd like to look at a specific part of the way the description is writen: "built to the specifications". At no point is it directly stated that the XIV hulls we find are leftovers from the XIV Battlegroup -- and gameplay-wise, they'd certainly be a lot rarer if that were the case. Currently it's "hand out in military surplus to commissioned auxiliaries at a slight premium price", which implies at the very least they can continue to be produced. This could, however, be a gameplay thing, because the XIV buff, while powerful, wouldn't be mechanically justified with the price & rarity increase that would be expected of the lore-accurate irreplaceable hulls.
Let's consider how ships are actually built in the first place:
1. Producing any kind of quality warship requires an industrial-scale nanoforge. Nanoforges are giant engineering nanite-powered factories that, via a very complicated human-assisted process, assemble raw materials into functioning starship components that can then be put together -- they must be integrated with the appropriate heavy industry in order to function. In order for a faction to express any kind of conventional power projection, access to such a nanoforge is fairly crucial -- the Hegemony and League both have pristine, state-of-the-art nanoforges, whereas the Diktat, Tri-Tachyon, and even the Luddic Church have damaged, 'corrupted' nanoforges that, while powerful, will wind up often producing components with substantial, but manageable, defects.
2. Nanoforges need instructions on how to build things. These instructions come in the form of 'blueprints' -- copy-protected, presumably encrypted data that includes the essential instructions on how a nanoforge could assemble functioning starship components. Blueprints are a prerequisite for the construction of a given starship.
As for what a XIV Battlegroup ship is, most of the adjustments are likely internal -- different 'structural modifications' that enable the mounting of heavier armour with surprisingly minor drawbacks on mobility. In the process, it marginally improves the base flux grid.
Manufacturing a XIV Battlegroup starship therefore requires access to an industrial-grade nanoforge, an appropriate XIV blueprint, the prerequisite raw materials, and maybe a specialist team skilled enough to put the components together. We know that raw industrial output is not a problem for the Hegemony: it has Chicomoztoc, a world with hundreds of millions of people equipped with a vast base of heavy industry and one of the sector's only 'pristine' nanoforges. Likewise, as a major faction with a large stake in the markets for ores and refining, it should at the very least be economically feasible to provide this nanoforge the material it needs to produce XIV starships.
The only issue, then, is whether the Hegemony has the blueprints and expertise to produce XIV starships. We can find XIV blueprints out in the wild, so I'm sure the Hegemony still has some lying around; likewise, it's difficult to believe that the literal descendants of the original 14th Battlegroup, under junta-based martial law, are clueless as to how stick XIV components together in the right ways.
As such, it's quite likely that the Hegemony can produce authentic XIV hulls. As others have pointed out, however, this process is clearly more costly and it's more economically viable to mass produce other ships to fill out the ranks. This would explain why XIV hulls are rarer and more expensive, yet also explain their relative proliferation throughout Hegemony markets despite so much time having passed since the collapse.