It follows that we have no primary sources for persons or events in Galilee in the 20s/early 30s.
But are you rejecting ancient historians' writings because written well after the narrated events?
(maybe these authors had primary evidence, but they were not telling. So that cannot be assumed, more so when some do not agree on the same event).
If you don't, you should not reject certain events in the gospels as unhistorical.
who their authors were or claimed to be, and we have in the case of the epistles only a name, Paul, with no independent means of assessing any of the internal claims.
But we can profile these authors through their writings, complete with biases & motives, and even, for some, other characteristics.
The first gospel written was in dialogue, it seems, with Paul,
That's an assumption. For examples, Capernaum, Nazareth, credited healing by Jesus, disturbance in the temple, "king of the Jews" do not come from Paul's epistles.
One does have to wonder at why other historians bother with any of the above rule
Ancient historians did not abide with all these rules.
These rules are idealistic, but that does not mean history of ancient times cannot be reconstructed with less data, as long as the overall result is not presented as a certainty.
Paul claims, according to many, that he learned about Jesus from other sources.
Assumption again. And what he learned from other sources (than human) are his gospel, alleged revelations from above, the OT & his own thinking. And that "learning" would be about the supposed resurrected heavenly Jesus, not necessarily the human Jesus.
So from where would he have learned about a Jew called Jesus crucified as Christ?
Not going outside Paul's epistles, a logical answer would be James, Jesus' brother.
Our aim is to understand they origins and nature of the epistles and gospels.
These questions cannot be answered with certainty and without controversy.