Going to be a long post.
In Mark 9:38-40 and in Luke 9:49-50, we have an interesting story where John the apostle tells Jesus about someone who does not personally know Jesus but is doing works in Jesus' name. John mentions how the apostles (or whoever "we" is) were insistent in stopping him. The mystery preacher is never named, but he has similarities to Paul (I'm not suggesting he is Paul). Jesus' response to John though, is that there's nothing wrong with this preacher and he is on their side. But Paul's later activity, and the problems he describe with churches not believing his authority, fits this mystery preacher. Mark and Luke have this story, but Matthew omits it interestingly enough.
Now, Joel Marcus in "Mark - Interpreter of Paul" makes a (in my opinion) valid case that the author of Mark is a "Paulinist". Cameron Ferguson in "The Oxford Handbook of the Synoptic Gospels" also argues that Mark 9:38-40 is essentially the author having Jesus justify the Pauline mission. It's interesting that this Paulinist has John be the one to attack Paul, rather than Peter or James. Paul in his letters only mentions John once but maybe they had bad relations or their churches had bad relations or maybe there's nothing, who knows.
Next we get to the author of Luke-Acts being a Paulinist. Well, just based on the focus of Paul in Acts, one could propose that the author is a fan of Paul. But can't jump to conclusions. Andrew Gregory in his essay review of "Acts and Christian Beginnings" looks at how Richard Pervo (I didn't want to mention him) argues for the author of Acts used Paul's letters to write. Lars Aejmelaeus also argues in "The Pauline Letters as Source Material in Luke-Acts" that this "Luke" figure used Paul's letters. Although I haven't seen much arguing for the gospel of Luke itself depending on Paul's letters but its dependence on Mark makes things messy. So we will only look at Mark as our representative of Paulinism here.
Now for the main point, there is a contrast here between Mark versus Gospel of John and 1 John. Mark seems to argue that you don't have to have personally met Jesus to be able to preach or do works in his name. The Johannine community appears to take the opposite stance. John has an eyewitness in the story, in contrast with Mark, which is purely coming from a narrator. John 19:35 is a random insertion into the crucifixion story to affirm to the reader that the story is coming from someone who was actually there and so he is trustworthy. John 21:24 tells us this is coming from a disciple of Jesus who is testifying (as in he was there) and his testimony is true.
John 20:24-29 at first seems to imply that "you don't actually have to see Jesus yourself, just believe" but its message is more complex than that. Verse 29 has Jesus tell Thomas he has seen him so he believes. Then those who believe the testimony of those who have seen are blessed for believing. But ultimately, Christian belief rests on the testimony of those who have seen. There is a hierarchy presented and the 2 other verses I gave as examples in the previous paragraph help enforce this point.
Furthermore, 1 John talks a lot about "what we have heard, what we have seen with our eyes, what our hands have touched". After that, the rest of the epistle gives instructions, gives teachings and combats docetism. Docetism appears to have been a big feature of a lot of gnostic groups, interestingly Marcion as well.
Finally, Revelation, though not usually seen as the same corpus as John and 1 John, has this interesting relationship with Paul as well. Revelation 2 contrasts with 1 Corinthians 8. Rev 2:14 bashes those in the Pergamum church who eat food sacrificed to idols. Rev 2:20 bashes those in the the Thyatira church also committing the same act. 1 Cor 8 takes a surprising position in that it seems to imply that eating foods sacrificed to idols can be acceptable (correct me if I'm wrong).
Interestingly, Ephesus is the only one of the 7 churches mentioned in Revelation that the Paulinist author of Acts has Paul explicitly visit, rather than just their vague regions. I have an interesting proposal about the author of Acts possibly disassociating Paul with the "negative" behavior of the churches found in Revelations by mentioning him travelling to their regions instead but that's irrelevant here and I don't have any sources that go into it.
To conclude my very long post, my question is, what do scholars have to say about the relationship between the Johannine churches and the Pauline churches? Feel like there's something there that's been smoothed over