GypsyComet
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The Ziru Sirka was larger than the Third Imperium, let us look at the demographics at the time the Vilani and Terrans encountered each other.
There were tens of trillions of Vilani, scattered across ten thousand worlds (more but the maths is easier) when the Ziru Sirka encountered the Terrans.
While the Ziru Sirka included what is now known as Julian space, it didn't include much in the direction of the Windhorn Corridor. The Corridor is rough going for J2, and the Vilani had enough to wrangle aready. So on the balance the First and Third Imperia are pretty close in geographic size and system count.
Using the Golden Age as a guide might or might not be appropriate, but it is worth noting that the most densely populated sector in context is Ilelish, and the majority of those multiple trillions are not Vilani, but Suerrat. Most other Imperial sectors pale in population comparisons to Ilelish. The Solomani end of things has a very high population in the Golden Age, but that's largely due to the Solomani, and wouldn't apply to the ZS.
That the Terrans and early Solomani were sending Shake-n-Bake colonies out in huge numbers to cement their gains in the Interstellar Wars is a factor too. Diaspora, Magyar, and Old Expanses owe a great deal of their modern populations to Solomani expansion three thousand years earlier, and a case can be made for that to extend, though tapering off, into Daibei and Massilia. GT IW informs us that the Suerrat were the masters of really good life support systems, Much of the Vilani colonial expansion to the final ZS borders was done with their assistance, and only after the Consolidation Wars. Prior to that was mostly Patent Enforcement fleets chasing "stolen" jump drives as far as they went.
Outside of the Imperial Core (the area "embraced" by the Rifts), the Vilani were likely not all that numerous.