Specifically, who overheard Jesus’ conversations with Pontius Pilate? Did Jesus tell the apostles about it afterward?
Don’t you suppose that during the 40 days after the Resurrection, the Lord might not have given His disciples some of the details?
And is it not likely that there might have been people (soldiers, servants, clerks, et al) in Pilate’s chambers who reported details to the first Christian community–maybe even these people converted themselves afterwards?
Pilate’s wife, Claudia Procles, was present at Pilate’s questioning of Christ, and sent Pilate messages not to condemn Christ.
Origen’s second century Homilies on Matthew suggest that she became a Christian, or at least that God sent her the dream mentioned by Matthew so that she would become one. Claudia Procles is recognized as a saint in two churches within the Eastern Christian tradition: the Eastern Orthodox Church and the Ethiopian Orthodox Church. In the Eastern Orthodox Church, she is celebrated on 27 October.
On Jesus before the Sanhedrin and Caiphas’s tribunal, Saint Anne Catherine Emmerich (sanctified by HH JP2) writes the following private revelation she had in entering into ecstasy in meditating on Christ’s suffering which at least sounds probable:
“Peter and John entered the outer court, in the dress of travelers, a short time before Jesus was led through, and John succeeded in penetrating the inner court, by means of a servant with whom he was acquainted. The door was instantly closed after him, therefore Peter, who was a little behind, was shut out. He begged the maidservant to open the door for him, but she refused both his entreaties and those of John, and he must have remained on the outside had not Nicodemus and Joseph of Arimathea, who came up at this moment, taken him with them. The two Apostles then returned the cloaks which they had borrowed, and stationed themselves in a place from whence they could see the judges and hear everything that was going on.”
Just 2 “possible” scenarios for how Jesus’ private conversations could have been heard.
It is very probable that Jesus Himself continues to narrate the gospel writers through his Spirit what happened on various occasions of his private encounters. One example is his temptation in the desert after he was baptized by John the Baptist. No one can eavesdrop at the place. If the latter-day saints (not the Mormons, but our age’s saints) were gifted by mysticism that enabled them to know some of his stories, probably the original Apostles would have, too. They are still receiving divine messages just as the Bible had said:
"And they went out and preached everywhere,** while
the Lord worked with them,** and confirmed the word by the
signs that followed."
(Mark 16:20, emphasis mine)