> John’s emphasis is on Jesus as God rather than a son of young Jewish parents.

Yep, but more specifically Jesus as the Logos, which is a core concept in Platonism and Stoicism.

John very clearly meant his gospel to be read by gentiles from a Greek background.

John to me as the youngest gospel, is an attempt to solidify what Christianity was becoming as it separated from the remains of Judaism after the destruction of the temple in year 70. It could have been written as late as 200 CE from what I have read. In my opinion that is why it diverges from the synoptic books. It had to address the new religion's theology more overtly as it had developed by then. Christianity was becoming popular quickly, once it became clear that pork chops were on the menu and surgery was no longer needed to join.