Yes, as I said they very clearly talk about how they changed the character completely between 1 and 2 in the book of interviews about the movies.
Having a ghost child mysteriously grow up after being stuck in a lake and having his mom go on a murder spree was a retcon specifically for a sequel, yeah. They retroactively changed Jason’s continuity for the sequels.
When was the last time you saw these movies? If it was recently we wouldn’t be having this conversation.