I wouldn't say the difference is quite that stark. Remember, the TSAB have the Arc En Ciel, which seems to be a standard for ships above a certain class, or that are expecting to face exceptionally dire circumstances. The fact they can install it whenever implies they fully understand it, meaning it isn't a Lost Logia and thus, is not something Ancient Belka had.
In spite of it's seemingly endless love for impossibly destructive super weapons.
They can build those, yes, but why do you think Belka couldn't? The only example we have of a Belkan warship is the saint's cradle, which was assumed able to stand off the entire TSAB fleet at once if it could get into position. They were only able to destroy it after Vita first destroyed its primary reactor from the inside.
But you're right, it's not a complete collapse. They've got the Library, and that has at least textbooks for probably just about everything -- if you can find them. The issue is the lack of living engineers.
See, modern civilization is highly interconnected. It's impossible for any country to stand on its own; the minimum population just to support all the specialties our technology requires just to maintain that technology, is probably a hundred million or more. Some companies do
really esoteric work. For example, there's only one company on the planet -- a small Japanese one -- that is capable of forging the containment vessels for nuclear reactors.
Pre-unification war Belkan civilization would have been even larger, more advanced, and more
vulnerable.
What happens to a civilization like that if you start ripping out parts of it? ... Well, it collapses. The war alone was catastrophic enough to do that; they lost probably fifty percent of their population, if not more.
After that sort of event, you can't just pick up the pieces and move on. If you don't have external support -- and they don't, the war involved every human nation in existence -- then you won't be able to maintain your technology and infrastructure.
What parts of it weren't destroyed by combat, will gradually run down and eventually fail because the people who know how to maintain it, and who know how to deal with that off peculiarity in manifold C and that the textbooks don't quite match the reactor design after a few too many patches... are dead.
To build new tools, first you need to rebuild your economy and put conditions in place for new, highly specialized groupings to form. But you'll be doing that while your existing infrastructure rapidly decays out from underneath you. So what do you do? You've got to do something.
Well, you look at your textbooks, and find simpler ideas. Older tools that might not be quite as good, but which are easier to learn about and which can be built by generalists. That's necessary; your economy is still fucked six ways to Sunday, and long supply chains would be a terrible idea.
Hence, you're returning to older technology.
This isn't a permanent condition. You've got the textbooks, and although many of the people who want to learn them will have to do so without the benefit of any tutoring, some are smart enough to do so. It is, however, something that might well take over a century to recover from. Multiple centuries, to fully restore the old world and replace all those lower-tech patches.
Mariposa showed up about seventy years after the TSAB was formed. Sixty years after the final aftershocks of the war, and she's looking at the first generation that considers their current state normal. She
is one of those lost pieces of technology.