Was Jesus’ human nature omniscient? It seems not by this:
This human soul that the Son of God assumed is endowed with a true human knowledge. As such, this knowledge could not in itself be unlimited: It was exercised in the historical conditions of his existence in space and time. This is why the Son of God could, when he became man, “increase in wisdom and in stature, and in favor with God and man,” and would even have to inquire for himself about what one in the human condition can learn only from experience. This corresponded to the reality of his voluntary emptying of himself, taking “the form of a slave.” (CCC 472)
However if the divine nature was omniscient how would that manifest in a given moment? Walking around interacting with the physical world and people, how could a person have thoughts and be omniscient and ignorant simultaneously? In a given moment you either know about germ theory or you don’t.