I think that as much as people compare D1 to D2/D3/D4, if you're looking for a D1 experience but modernized you'll in general find much more of that in the roguelike/roguelite genre these days than in any of the Diablo sequels, since D1 was more of a roguelike than an ARPG. I don't know of any roguelikes that have done horror anywhere near as well as D1 (and I also think that D1 is somewhat inextricably linked to the time it was released), but I think the game I've played recently which I consider the closest to D1 overall is actually Hades, despite its pretty drastically different tone and superficially different gameplay/UI/etc.

(This isn't a knock on the other Diablo games: D2 was one of my most played games, I play D3 to this day, and I'll no doubt play a lot of D4 when it comes out)