To reconstruct 2nd century cultural literature context of Roman satire in Early Christian texts, it is useful to learn why Paul's letters do not give a good indication of what the cultural literature context is in Early Christianity.
To illustrate the problem of Jesus' historicity, try imagine that 100 years before Plato, a person claims to know one family member of Socrates, but only seen Socrates in a vision. 100 years later, Plato writes about Socrates as a historical person that lived a century earlier.
Furthermore, Plato portrays Socrates a man advocating eunuchs, with superpowers that can heal the blind, turn water into wine and raise people from the dead. Normally, people would think about this as "that vision is like a feather turning into 10 000 hen".
It is not unreasonable to think that Socrates might have existed in this context, but surely you can imagine that all the supernatural stuff might come from somewhere else. People telling stories that grow more amazing over time, adding more and more unrealistic stuff.
Now, let's say the Greek authorities suspect Plato's teachings for being fabrications and accuses him of advocating cannibalism in the form of transfiguration of wine into Socrates' blood by a mystical ritual. At this point, most people would think "WTF?".
In response, the cult of Plato claims that the person who once knew a family member of Socrates and saw Socrates in a vision, is the only authentic origin and all the other cults that also believe in Socrates having superpowers and use the same transfiguration rituals, are fake.
Next they claim that a star impregnated a virgin who was the mother of Socrates and three wise men from India came to give gifts to baby Socrates who was born under a huge tree in the forest. They take over the power in Greece and start persecuting everyone who makes fun of them.
700 years later, a school is established to prove that Socrates indeed existed historically and the facts about him were historically accurate. However, to avoid controversy, they make people sign contracts to not dispute Socrates' historicity in order to hold teaching positions.
After 200 years of studying the texts, analyzing their composition and lexicography, carefully deconstructing the myths according to naturalism, they firmly agree that the person, once knowing a family member of Socrates and saw him in a vision, lived 100 years before Plato.
Now, there is a guy who got interested in this stuff and thinks "Hmm... that person only saw Socrates in a vision. Perhaps he thought of Socrates as an angel which did not existed historically?"
The school that spent 200 years studying this goes bananas.
"You are just a fringe theorist!" they claim. "Look, that person knew a family member!"
"Like the other family member, that supergiant goddess angel who cried tears that became the ocean?"
"No! The REAL family member!"
"Hmm... I think I can show you using Bayesian probability theory that the person might have not believed Socrates was an actual person"
"Your Bayesian priors are wrong! The reference class of mythological figures that once existed historically is larger than those who didn't!"
Next thing that happens is another guy, but this time a credible scholar, who shows that Plato might have been writing about a Socrates without having good sources going back to the person who once knew a family member of Socrates and claims to have seen Socrates in a vision.
A lot more people notice the controversy and gets drawn into the debate. They say:
"OK, calm down. Can't we just all agree that these stories about Socrates having superpowers might come from somewhere else?"
"No! Socrates has to go back to that person who saw the vision."
The point of this story is to illustrate that Paul's original letters do not tell us much about Jesus. Therefore, the logical conclusion is that most claims about Jesus must come from somewhere else.
We don't know where people got their claims from, but it could be a mixture of historical and mythical origins.
In science, there is no such thing as an "authentic Jesus" going back to Paul. All claims that people make about Jesus are just claims, unless they can present some evidence.
The idea of tracing back authenticity of the historical Jesus to Paul is an idea leftover from the time when people were persecuted for believing in Jesus and performing similar rituals, but did not believe in the authentic origin of their religion through Paul.
However, when doing science, one has to ask what is the cultural literature context of Early Christian texts. We have hundreds of such texts and they contradict each other. Paul's letters in this context is mostly irrelevant, because they only contain a fraction of the claims.