Innovation-averse Vilani would be the least likely to survive. Vilani who returned to their ancestor's drive for innovation, exploration and expansion would be most likely to rebuild.
Once again, the majority of the Solomani Sphere worlds had never been part of the Ziru Sirka or the RoM that followed. Individual Terran countries and companies explored, colonised and settled in the opposite direction to the Imperium. The Sylean Solomani may have claimed a unified Solomani Sphere as their birthright, but the truth was the Terrans didn't even call themselves Solomani. The Solomani Sphere is another fiction, the Solomani Confederation is of no concern to Terrans settled far to Rimward. It is an Imperial conceit that the Terrans even want to rule the Third Imperium.
By the way according to the wiki Syleans make up the majority of the population of Sylea:
"Eighty billion sentients inhabit Capital, mostly members of
Humaniti, a number which has remained fairly constant through the entire
Third Imperium.
- Of these, thirty-six percent are primarily racial Vilani, eleven percent are Solomani and fifty percent are native Syleans, and the remaining three percent consists of a mixture of various human and non-human minor races.