Yeah it should come out as a separate update in a few hours I think is the current schedule, expected it to come out last week with 1.09 having been the patch adding compatibility for the DLC itself but the only thing that happened was that it accidentally leaked out on XBox One systems so it's likely been done for a while now.
(And here's 1.10 with a few fixes for it and some other additions and general bug fixes.)
Much of the shared content should be in the game files already by now (Likely for use in the arcade map editor.) but the rest will probably come in the form of a download adding the dlc_zombies folder and some files to the FarCry5\data_final\pc\downloadcontent\ location next to the existing dlc_vietnam and dlc_mars content packs.
Update also added the Rook outfit from the intro but it's locked behind New Game+ completion and the new difficulty level they introduced to the game. And once the DLC is unlocked I guess a few of the new weapons and vehicles from it might make it over to the main game again once the DLC has been started which tends to be the condition for how that works.
EDIT: Well I suppose it's a reward of some kind for players going through all that again and on a new difficulty level too but for a primarily first person perspective game it's not going to be too noticeable.
(Well there's an achievement and Ubisoft somehow seem to have resisted making it a UPlay club one with some 10 reward or whatever and using it to unlock bonus content via the client software.)
EDIT: And there's a 170 MB update, pretty small but it looks like it's out then? Huh must have had most of it in the shared content already this time for this add-on.
