I'm a little late to this but I cannot recommend early 00s horror enough! If you want a good psychological horror game I 100000% recommend Demento/Haunting Ground. It's a psychological stalker survival horror and I adore it to no end!! (I'm totally not biased bc my profile is Haunting Ground themed I promise-)
Other games like Silent Hill 2 and 3 are pretty good too! Not as focused on the psychological sides but they're very good survival horrors :3
There's also Rule of Rose and Forbidden Siren but I'd recommend watching a livestream/playthrough instead because they're pretty... uh... well they're pretty hard to play.
Unfortunately those are all PS2 games and they're all abandonware so you'd likely have to get an emulator to play them, but I honestly recommend it because they're amazing games!
If you want a survival horror experience that you don't need a PS2/emulator for then I'd 100% say to play Pathologic. It's awful and you'll hate it. 10/10 survival horror :3