Not even NT authors corroborate a single Epistle from Saul/Paul or mention a so-called Pauline Church.
That's nonsense, because only one book in the NT is concerned with Paul at all, without being by Paul: Acts.
For the gospels it's not even in the time frame they're writing about. So basically demanding that they write something about Paul or really the church 20 years after Jesus, is as bloody stonking stupid as demanding that War And Peace, whose epilogue ends in 1820, and whose main action ends even earlier, mentions the tsar's death in 1825. I mean, if Tolstoy knew that, he must have written that in the book, and if he didn't, it's proof that Alexander I is made up. That's the kind of nonsense logic you're applying.
And Acts being a novel, frankly, if you want to decide exactly what goes into it, then write your own novel. Presuming to know exactly which mundane details the author would or wouldn't include, without even knowing for sure who that author is or any context really, is just bloody stonking stupid.
Plus, generally, it's not the kind of thing that went into that kind of documents. If you read Josephus for example, hardly any letters are ever mentioned about ANY of the characters involved, even when realistically that would be the way they got some piece of information.
But generally, you didn't mention every time one of your characters went to the loo, or sat down and wrote something. Ancient books, especially novels, were NOT the modern kind of 200 page sprawl, where even the character stopping in front of a mirror or opening a book are mentioned as flavour details. That kind of sprawling, intertwined story only appeared after mass produced paper and the printing press made it be even viable at all. Acts has a total of 28 pages, for example, and only slightly over 12 of them are after Paul's vision in Acts 16. That's it. The whole story of Paul after his conversion is a mere slightly over 12 pages. By modern standards it wouldn't even be a novel, but a rather compressed short story. They just didn't have the SPACE to include every arbitrary detail you can think up.
And more specifically it doesn't fit Luke's style. For example, in Acts 20:17, it just says, "
From Miletus, Paul sent to Ephesus for the elders of the church." Realistically it would have involved sending some kind of letter summoning them. But Luke doesn't feel a need to include that message, nor what form it was in.
But to return to the actual information density in the classical world, we're already in the middle of Paul's way back to Jerusalem, a mere 4 pages after his conversion. We're talking an average of several years of the story per page. But anyway, that's flippin' it. That's the space in which you apparently expect it to mention every single detail of what Paul did, including every time Paul sat down to write some letter.
So on the whole my impression is that basically you don't actually know that kind of details, and generally aren't qualified to be making that kind of analysis. You just make up whatever BS 'criteria' as you go.