But don't ya think the pronouncements to the crowd would have been in Koine Greek ?
It’s a debatable question.
It would have been infra dignitatem for the procurator to embrace the language of the barbarians in any official correspondence or record of legal proceedings.
Bilingualism and multilingualism were common at that place and time, though. It’s easy to imagine some scribe standing beneath him translating back and forth to preserve the fiction of Roman indifference to the barbarians, even though Pilate and the crowd in fact spoke each other’s languages.