With Universal and Paramount having a really good bedside relationship with AQP and this for HHN, Star Trek for FFN, and SpongeBob for Kids; I am not surprised they're opting to keep it contained to the original films before New Line. Less red tape to go through.
It's probably more to do with the tricky rights. I did another deep dive to check. From my understanding, New Line (curently a sub-division of Warner Bros) has ownership of the Friday the 13th name and the ability to make future movies as long as the other two rights holders play along (which collectively is "Jason Universe" -- both Victor Miller & Sean S. Cunnhingham/Horror Inc. -- seperate parties joining together for the sake of making money off of this franchise in the meanwhile until they figure out how to split the money for future movie installments).
Victor Miller solely has the rights to the first F13 film and everything therein (Pamela Voorhees, young Jason, Crystal Lake, etc.), which is how the Crystal Lake TV show is being made.
Sean S. Cunningham/Horror Inc. solely has the rights to everything else in the franchise, which specifically includes mask-wearing adult Jason (because that iteration of Jason didn't show up until F13 Part 3). However, Horror Inc does not own the F13 trademark and branding. Who does?
New Line owned the trademark on F13 name and branding, then ofcourse their films JGTH, Jason X, and FvJ. New Line and all of their assets were bought by Warner Bros and that's when the F13 remake was made (with New Line now being a subdivision of Warner Bros). That film was a co-production with Paramount, who claimed they owned the original film, so therefore they needed to be involved (this is probably where Victor Miller started to get pissed off and decided to take legal action because the movie made bank and he did not have ownership at the time).
Paramount regained the rights for a short time in the 2010s, but nothing came of it because of questionable rights issues that Victor Miller started to stir up and a crappy horror market at the time (this era is not super important, but worth noting).
The rights reverted back to New Line/Warner Bros, and they currently have the rights to make further movies in the franchise, who has happily partnered with Sean/Horror Inc. in order to do so, as that is how things were traditionally done until Victor Miller stalled things to get his piece of the pie.
And after a long legal battle, Victor won the rights to the first film while Sean/Horror Inc. continued to own everything else. Jason Universe was formed between Victor Miller and Sean S. Cunningham so that Jason could continue making money through multiple avenues. However, they both still can't agree how the money should be split on future films, so there's a delay on that aspect until further notice.
While Jason Universe is more ancillary stuff regarding the franchise (merchandise, games, live attractions, etc.), HHN probably still can't show content from the New Line films without New Line's say so as they are the THIRD rightsholders in this situation. They (HHN) probably only acquired the rights solely from Jason Universe, as that was expensive enough, which means they can only use content from 1-8.
So JGTH, FvJ, Jason X and the F13 remake can be included if New Line plays along too. But for a movie to be made (and a maze on ALL the properties), Jason Universe (Victor Miller and Horror Inc.) and New Line all need to be on board.
Looking at F13's inclusion at HHN over the years, my guess is they only needed the rights specifically from New Line/Horror Inc to do mazes without the involvement of Paramount. I remember specifically in 2007-2008 while in line for the F13 maze, they were showing clips from the movies, but they were only showing JGTH, Jason X, and FvJ. Which I thought was a strange choice because most of what the mazes entailed was content from the Paramount movies. In 2010, the F13 maze was for the remake, thus New Line/Horror Inc.. And the 2017 portions of Titans of Terror was a mish mash of the mainline series on the Terror Tram and remake Jason in the maze -- New Line did not own F13 at the time, but Horror Inc. did, so HHN probably only had to go to them for that year (unless Paramount also had theme park rights during their brief ownership of the rights again at that time -- which is possible).
So unless New Line is involved this year, which it sounds like they are not, it's very possible we WON'T see the bed kill as I previously thought because that is specifically from FvJ (a New Line film) -- unless they can argue it's generic enough and the character being killed is not the character from that FvJ scene.
So it does not seem Paramount currently has any rights to F13, Jason, or any of the world.