Since The Talmud didn’t come into existence until Centuries AFTER the Jewish Authorities handed Jesus over to Pilate to execute Him, that understanding can not in any manner - dovetail with Sacred Scriptures/NewTestament/Gospel.
As Catholics . Sacred Scriptures are The GOTO for Source Info the Crucifixion
Source Info from John
The Jewish leaders took Jesus from Caiaphas to the palace of Pilate who came out to them and asked, “What charges are you bringing against this man?”
“If he were not a criminal we would not have handed him over to you.”
Pilate said, “Take him yourselves and judge him by your own law.”
But we have no right to execute anyone,” they objected.
Pilate summoned Jesus and asked him, “Are you the king of the Jews?”
“Is that your own idea,” Jesus asked, “or did others talk to you about me?”
“Am I a Jew?” Pilate replied.
“Your own people and chief priests handed you over to me. What is it you have done?”
Pilate went out again to the Jews gathered there and said, “I find no basis for a charge against him. But it is your custom for me to release to you one prisoner at the time of the Passover. Do you want me to release ‘the king of the Jews’?”
They shouted back, “No, not him! Give us Barabbas!”
Then Pilate took Jesus and had him flogged. .
Once more Pilate came out and said to the Jews gathered there, “Look, I am bringing him out to you to let you know that I find no basis for a charge against him.”
As soon as the chief priests and their officials saw him, they shouted, “Crucify! Crucify!”
But Pilate answered, “You take him and crucify him. As for me, I find no basis for a charge against him.”
The Jewish leaders insisted,
“We have a law, and according to that law he must die, because he claimed to be the Son of God.”
Pilate said. “Don’t you realize I have power either to free you or to crucify you?”
Jesus answered, “You would have no power over me if it were not given to you from above. Therefore the one who handed me over to you is guilty of a greater sin.”
From then on, Pilate tried to set Jesus free, but the Jewish leaders kept shouting, “If you let this man go, you are no friend of Caesar. Anyone who claims to be a king opposes Caesar.”
It was the day of Preparation of the Passover; it was about noon.
“Here is your king,” Pilate said to the Jews.
But they shouted, “Take him away! Take him away! Crucify him!”
“Shall I crucify your king?” Pilate asked.
“We have no king but Caesar,” the chief priests answered.
Finally Pilate handed him over to them to be crucified.