This indicated that Paul, living during the time of eye witnesses, had access to much more information than in the Gospels.
Now there are also many other things that Jesus did. Were every one of them to be written, I suppose that the world itself could not contain the books that would be written.
(John 21:25, ESV)
This shows that Paul's information about Jesus wasn't limited to the Gospels. This has additional details compared to the Synoptics.
For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread, 24 and when he had given thanks, he broke it, and said, “This is my body, which is for you. Do this in remembrance of me.” 25 In the same way also he took the cup, after supper, saying, “This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me.” 26 For as often as you eat this bread and drink the cup, you proclaim the Lord’s death until he comes.
(1 Cor. 11:23–26, ESV)
While the Gospel of John was written after Paul's letter, it still gives us some information about Jesus' testimony to Pilate that centered on being truthful.
So Pilate entered his headquarters again and called Jesus and said to him, “Are you the King of the Jews?” 34 Jesus answered, “Do you say this of your own accord, or did others say it to you about me?” 35 Pilate answered, “Am I a Jew? Your own nation and the chief priests have delivered you over to me. What have you done?” 36 Jesus answered, “My kingdom is not of this world. If my kingdom were of this world, my servants would have been fighting, that I might not be delivered over to the Jews. But my kingdom is not from the world.” 37 Then Pilate said to him, “So you are a king?” Jesus answered, “You say that I am a king. For this purpose I was born and for this purpose I have come into the world—to bear witness to the truth. Everyone who is of the truth listens to my voice.” 38 Pilate said to him, “What is truth?”
(John 18:33–38, ESV)
This is probably what corresponds to the testimony the same time as the Synoptics.
The Jews answered him, “We have a law, and according to that law he ought to die because he has made himself the Son of God.” 8 When Pilate heard this statement, he was even more afraid. 9 He entered his headquarters again and said to Jesus, “Where are you from?” But Jesus gave him no answer. 10 So Pilate said to him, “You will not speak to me? Do you not know that I have authority to release you and authority to crucify you?” 11 Jesus answered him, “You would have no authority over me at all unless it had been given you from above. Therefore he who delivered me over to you has the greater sin.”
(John 19:7–11, ESV)
The problem Jesus faced was, if he fully defended himself, he probably could have escaped crucifixion. Thus, Jesus answered truthfully, except he did not answer Pilate's question, "Where are you from?"
Paul, often jailed for his preaching Christ, evidently drew strength in Jesus' example when on trial. In Acts we have example of Paul giving his testimony while on trial, even his inviting them to follow Christ.