I think the City can resurrect the Children of the Vault as a direct parallel to the mutant resurrections using the Five. It seems like the the Vault and Krakoa are engaged in a superhuman arms race trying to outdo each other. We see that the mutant resurrections results in upgrades to mutant powers and in the first issue, Serafina was upgraded by the City.
The Vault is probably a tesseract where the interior space is larger than the exterior space.Also I don't comprehend how the City operates, if Aguja can detonate it to smitherines.Is it a projection or an actual material construct?I'm guessing it's sort of like the matrix that can reboot and reconstitute itself coz all those 3000 children nuked seems unlikely.