Vilani worlds with considerable Terran presence researching TL13?
It's the only explanation that's plausible.
A slightly more nuanced interpretation would be that there are (a handful) Vilani worlds scattered around that "went rogue" on technological research once they learned that TL=B
wasn't the limit of possibility. Sure, it would be breaking the straight jacket of Vilani custom and practices to "stay in your lane, never do more than you're told to do" (etc.) ... but that can be rather easily explained via "corruption of norms" brought on by "cultural contamination" of Solomani ideas of How Things Ought To Be getting blended into Vilani culture.
If the Game™ won't let you "win" ... change the Game™ being played ...
It doesn't have to happen EVERYWHERE (all at once?

) ... but it can happen in a few places, where Mad Scientist/Mad Engineer types decide to "push the envelope" of what can be done with technology. The society at large remains TL=B-C, but some research into TL=D possibilities is taking place ... some of which survives the Long Night to become archeological finds later once the Third Imperium emerges from the Long Night.
And given the location of the Sylean Federation (that becomes the Third Imperium), it "makes sense" that these isolated finds of TL=D prototypes (not all of which remain in working order) would tend to crop up on (formerly) Vilani dominated worlds.
After all ...
"In every revolution, there's one man with a vision!"
The problem is ... not all revolutions are successful.

One man cannot summon the future ... but he can change the present.

But he must also have the POWER ... and there are no guarantees of that ...
Remember, evolutionary pressure doesn't "try" to do the
One Thing That Will Succeed™ ... instead, evolution tries EVERYTHING in parallel, including things that WON'T succeed, using a vast sample size (and lots of experimentation) ... and then lets the chips fall where they may ...
wash, rinse, repeat. This means that there won't be a single attempt at advancement, but MANY ... and MOST of them will fail to catch on and take hold/rise to prominence (and/or dominance).
Those ... failures ... to reach TL=D are what are scattered around in (former) Vilani space, lying dormant until (re)discovered in the present time.
Breakthroughs are always possible ... but you still have to contend with the
"Burn The Heretic!" crowd who reject change that they cannot control or do not sanction.
