You’re confusing the ability to do a thing… with the recording of said thing. Pilate might have made a note of it in his personal records, but it was never sent back to rome. Being a citizen entitled one to a full trial which comes with records of that trial.
As a non-citizen he would have never constituted more than a footnote.
As for the Sanhedrin…. They had a long history of having upstarts knifed by “loyal” mercenaries. Makes one wonder, right?
Of course this changes nothing- there are no records contemporaneous to jesus that survive today indicating the jesus-of-the-bible actually existed.