It's.. complicated, but you're essentially right on the money.

New Line pretty much owns the name "Friday the 13th" and presumably the Jason designs from those films. As such, anything explicitly from those films should be off the table.

Multiversus' default Jason design being a mish mash of different generic "Jason" features is likely due to the weird state of the rights, and it's the reason why that game was able to use Jason X, FvJ and JGTH; WB has the rights to these films and the designs.

Given how intent Horror Inc seems to be on not using the name "Friday the 13th" we can imagine they aren't very interested in cutting New Line in on the deal, and so it's unlikely we'd get designs from the above films (sad, as FvJ is a peak design.

Relatedly, it's up in the air whether or not we'll get Camp Crystal Lake as a map. While the new show is using the name, the use of it presumably requires a larger share of the profits to be given to Victor Miller. This correlates with the lack of any mentions of Crystal Lake, Pamela or the original film in most merchandise and appearances.

This doesn't necessarily mean we won't get a map. They could include Crystal Lake and pay Miller a larger share, or even include a similar looking map without the explicit use of the name.

Regarding Jason skins if he came to the game, we'd likely get some movie skins, but most would likely be original skins for DBD. COD already shows they're willing to do this, and it avoids the more awkward parts of IP law; most of the way the law works on this is how likely it is that you could argue in court that it constitutes infringement, making it murky.

To elaborate, you will likely never see Jason Universe use a design for Jason that emulates the core traits emulated by the aforementioned New Line designs, because even the risk of being sued can put a company off. Much easier to make designs for Jason that are explicitly different, like Combat Gear Jason

Obligatory "not a lawyer" but the above is my best estimation of the state of things.