That theological doctrine about the holy spirit comes from the later Christian writings, which you're taking to be straightforward, reliable historical reports. Critical historians read the texts much more objectively than that because they're interested in separating fiction from fact, legend and myth from history.

No, the criticism isn't just that the four gospels were written decades after the fact. It's that they were written anonymously, they were highly redacted over some centuries (only scraps survive from the first half of the second century, and none survives from the first century), and most tellingly, they built on each other, which demonstrates that they weren't written by eyewitnesses. Are you familiar with the synoptic problem in New Testament studies?

https://en.wikipedia.org/wiki/Biblical_manuscript#Earliest_extant_manuscripts