IMTU the reason for the sudden surge and long stagnation of the Vilani grabs some of the OTU stuff and then wanders into speculation.
(IMTU stuff so ignore if you don't like
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In V&V they mention an ancient war machine that was still quasi-functional (it appears again in 1248 to shoot up the black fleet), but was damaged and trapped for millenia. Now would a super smart AI machine sit on it tracks and idle away for 300,000 years? Not likely.
In the past some of the Vilani found a communicator which allowed contact with this war machine. By this stage the war machine was very low on power and could only remain cognizant for short periods of time, so it formulated plan to advance the Vilani's tech enough to perform repairs and recharge it. Once repaired it would continue on it's original mission (aka Destroy everything).
The downside is that the critical power situation only allowed brief periods of contact and passing on tech advances. The machine would then power down and recharge slowly till it had enough for another 'revelation' for its minions.
To maintain secrecy (other war machines may be listening) and to keep their own power, a semi-religious priesthood was made. The inner circle of the priesthood knew the basic secrets of the tech, while everyone else was monkey see, monkey do. This priest caste evolved into the researcher caste, the inner circle into the 4 bureaux, and the Vilani's aversion to knowing anything about how a machine actually works is a holdover from hundreds of years of enforcement of the secret (do not question or we do nasty things to you).
This plan was puttering along slowly until the war machine suffered a critical power failure, and didn't reboot. The Vilani's benefactor had gone silent.
The researchers scrambled to actually understand the tech they had been given, and any new 'discoveries' came to a screeching halt. At this point the locked down independent research hard as they could no longer be guaranteed the edge in tech development. After long and steady progression the Vilani empire ground to a halt and began to decay.
Then along came the Soli's and the rest is history.
Of course somewhere out there the communicator still exists, and perhaps the war machine has garnered enough emergency power and is awaiting its reboot command.