The possibility is that despite it being a nuclear conflict, the number of strategic weapons had been downgraded sufficiently at that point that almost all strike capability was expended on counterforce targets rather than countervalue targets, leaving most countervalue strikes to lower yield weapons which maybe just took out the portions of metropolitan centers with EMP destroying a lot of the infrastructure, but without completely incinerating the cities. This might particularly be the case if there was some warning about this possibility, people might construct shelters and ABM systems to protect large economic centers so they wouldn't bother taking out the city proper, but rather try to cripple it with a high atmosphere strike.
That could explain why things seemed so backward, but that cities largely remained habitable and rebuild in time. There was probably a lot of latent human industrial capability that was just looking for the political will to unite and rebuild rather than continue on in the post-atomic horror situation of nothing working.
The Vulcans might have come and helped patch up the human electrical/information infrastructure, and was then shocked that the countries banded together so quickly to rebuild and putting aside old hatreds/changes. I mean if we take the Vulcan's Soul Trilogy at face value, Vulcan was so riven by state conflicts that they were still working at city-state level despite being at roughly 21st century/22nd century tech levels. So the ability of humanity to go beyond that quickly might have been unexpected from their experiences.