To piggyback on this, here is some more high level details: the rights ended up in a legal battle between the screenwriter of the original movie, and the producer of the movies. Everything was frozen for a decade of battles. The writer won the rights eventually but only for the original movie and he is the one working with Peacock for the Camp Crystal Lake show. The movie producer owns the rights to the sequels. This is tricky because the well known mask wearing adult Mutant Jason was not in part 1 but his backstory is so it get's messy if they do not work together.
They may move forward separately on their own projects referencing what they own and if so we may get altered stories. Since the writer only owns part 1, he can only reference from that hence why Camp Crystal Lake is a prequel and sounds like it focuses on Mama Vorhees and may not include an adult Jason at all. Since the Producer owns the rights to the sequels, he could eventually make a new movie that does not reference the first movie at all. So it would have to be Jason with a new last name (or no last name) and different location names, etc.
All in all it is a very unfortunate situation especially since we are in a time where nostalgia horror sequels are doing very well.