i have no nostalgia for this game given i properly played it for the first time around 2016 or so but still consider it incredible, so i guess i'll chime in
The mood and atmosphere are very distinct. from the second you get out of the car or even in the cutscene before, everything has such an interesting coloration and effect to it that makes you feel like you're in a truly 'unsettling' place.
Then you have the game's ability to put dumb cheese humor, actiony stuff and horror elements together in a surprisingly well put-together way. all of it feels natural and 'right' in the world and makes it all enjoyable to experience, and that's a really tough balance to make. almost all other REs go for a similar effect but it doesn't quite work out. RE5 and RE6 being big offenders here.
The pace at which new content comes your way is very, very strong. it consistently hits you with brand new areas but also gives you just enough time that you feel comfortable and 'settled in' before you continue to new areas.
this specifically is a big deal for how memorable and strong a game ends up being. too slow of a pace kills the enjoyment of new areas as you feel them dragging, but too fast of a pace means you're just going from area to area without regard to how they're like.
compare the village section or the castle section etc from RE4 to almost any section in RE3R for example. the major difference in how the games are paced and area distribution makes areas in RE3R feel conjoined and melded together without as much of a unique identity.
Then you have the moment to moment gameplay. yes, the controls will feel dated but they're fine-tuned to meld with the gameplay, rather than simply following a 'standard'(as there was none at the time).
this means enemies are specifically catered around your limitations. this allows even slow, trudging zombies and unique types of enemies like the Regenerators to be genuine threats, and additionally keep with the horror aspect of the game. going too hard on 'fast-moving' enemies can make them feel more like action-game enemies, so this strikes a good balance of horror and action.
additionally, this creates tighter moment-to-moment gameplay. because of your inherent limitations, you have to be much more careful around enemies, be very wary of their locations compared to you, and be sure not to take on more than a couple at a time else risk being mauled, or focus on strategically using your physical abilities for crowd control.
this is all just a consequence of running and gunning not being a thing. it can make that big of a difference.
There's more as well like the NPCs unique charm(like how the Merchant is a favourite despite his very strange disposition, purely due to the game's established unique tone), the excellent balance and pace of getting new strong weapons and upgrading, the emphasis on collectibles that genuinely mean something and are organically findable by keeping an eye out, the near-invisible dynamic difficulty allowing weaker players and stronger players to both have genuinely satisfying experiences, and a lot more.
There's a ton to love about this game, and i don't believe it became a classic to be copied for generations by any mistake. even coming to it as barely even an RE fan over a decade after it came out, i found it to be something special.