Firstly, I must say I think you understand what a ‘summary’ is, if you think the four gospels are not summaries of Jesus’ teachings and ministry…summaries are not every little bit of information in the original. They are brief, they are concise. John 21:25 even says that there was much they could not write - but it is indeed a summary.
Secondly, you misunderstand what the “gospel”, or the “good news” is, if you think that the New Testament does not contain it fully.
Look at all the times that the term is used in the New Testament.
Do any of them sound as if they mean “the entire life and teachings, and every single word spoken by Jesus”?
Or are you talking about some other gospel? (Galatians 1:6-9)
So, what is the gospel then? Galatians 3:8 suggests that it has something to do with all nations being blessed through Abraham. Ephesians 3:6 tells us that through the gospel, gentiles become heirs with the Hebrews. How does Paul summarise the gospel? In 2 Timothy 2:8, he says “Remember Jesus Christ, raised from the dead, descended from David.” The gospel, the good news to all mankind, is that Jesus has died so that we may be reunited with God!

that is simply circular logic mixed together with a good dose of begging the question.
Well, as far as large portions of it go -
2 Peter 3:16:
He writes the same way in all his letters, speaking in them of these matters. His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction.
Peter calls Paul’s writings “Scripture”. Is Peter’s word good enough for you?