Does Outlast 2 on GOG have the 2018 patch they announced on Steam that added the new story mode, but the actual part I want to know about, the cut content, and if it does, how do you access it?

Here you can read the changelog for the last patch which has been released here on 27 March 2018.

Thanks. I had read that, but I wasn't sure if it was just someone mentioning the newest update to the game even if it wasn't on GOG, or if it actually was in the game. Because every place that talked about the update never mentioned GOG, only Steam.

I don't own the game on GOG, but, according to gogdb.org, the changelog I shared is referring to an actual update that has been effectively released on GOG.