There's so many I could recommend, but if really dipping your toes into older horror games for the first time (and already tackling the Silent Hill games), then some I'd throw out there (a few of these I'm keeping your taste in mind as well). Going to limit myself to the PS1/PS2/Dreamcast so I don't go overboard, and know there are more games on these platforms I'd recommend but I'm going to toss out some of my absolute favorites and some others I think you may be able to appreciate Jawie. I'm going to try and limit myself to 10-12 games.
This is in no specific order.
Hellnight: This game is simple but I really like it. First-person dungeon crawler with a few point'n'click bits (but very simple) where you get chased by a single monster that slowly mutates and evolves as the game goes on. Story branches based on who you have with you in a sorta' partner perma-death system. Story is pretty tame until the last third of the game, where it goes into very odd places.
Nightmare Creatures 1 & 2: These were old action-horror games, they may be a bit dated by today's standards but they're still pretty creative and fun, and are among the first action-horror games to exist in the 3D space, so I feel you might get some appreciation for them Jawie.
Fatal Frame games: See others are recommending them, but yeah Fatal Frame games are worth playing FF1 is flawed but has good stuff. FF2 is the fan favorite, but FF3 is my personal favorite. Fatal Frame despite not selling as well often gets mentioned in the same breath as Resident Evil and Silent Hill for a reason, it's well done for what it is, and the camera combat is a lot more fun than it may sound on paper (I think you may actually really like this one, it's got kinda' a point system not too dissimilar to Dino Crisis 2's, but per ghost encounter rather than per room).
Illbleed: This is a zany one and one of the weirdest games you'll play. You enter a horror amusement park to save your friends (who you can unlock to play as) and use a horror monitor to progress. Gameplay is weird, game doesn't always explain what to do, gameplay is so-so, but this game makes up for all of it for just how absolutely batshit insane this game actually is. You go to six different "attractions" each with a B-Horror movie plot, and each one with quite a bit to surprise you with.
The Suffering: There's also a sequel. It was a PS2/Xbox/PC action-horror game where you play an escaped convict on a prison island where Hell has been set lose and you go guns blazing through horrors somewhere between demonic and psychological. I think you'd get some enjoyment out of it.
Carrier: One of SEGA's attempts at a Resident Evil killer on Dreamcast. It's pretty decent actually, not RESIDENT EVIL quality, but it's got some interesting things (like there's survivors you can save or lock onto and accidentally kill if you mistake them for enemies coming at you). Has plant based enemies on a boat, but better boat setting than the RE games.
Cold Fear: This was kinda' a spiritual sequel to Carrier by some of the devs (and an older game, Deep Fear). Came out after Resident Evil 4, it plays somewhere between RE4 and the older Re games, but also set on a boat/oil rig. Rough spots, but it has its moments. Does this weird thing where it mixes behind the shoulder camera when aiming and in certain areas, but fixed camera in some areas you explore.
Extermination: This one you may personally enjoy, some of the people that worked and wrote the older Resident Evil games worked on this. It's kinda' a poor man's Resident Evil meets Metal Gear, but the novelty of a game somewhere between Resident Evil and Metal Gear still gives it appeal.
Kuon: Game by From Software before the Souls game, it's a sorta action-horror game in ancient Japan where you use spells to fight monsters in a Resident Evil-styled game. Three different character stories to go through (two main ones and a "final" unlockable one)
Clock Tower 3: You listed Haunting Ground, make sure you check out CT3. Haunting Ground is the better game, but CT3 is the older game that inspired it, and it is one of the funniest horror games you'll ever play. It was the first game Capcom used motion capture on, and the person who directed the cutscenes and story was a Japanese film director who loved this one type of Japanese overtly-express drama theater, and it fucking shows and the story is actually hilarious involving you becoming a magical girl to fight the ghost of murderers. I think you'd appreciate it.
I see someone mentioned Galerians, I'd recommend it too. It's an old PS1 Horror-RPG but you get psychic powers to blow people's heads off and it plays a bit like a Resident Evil game but with some RPG elements (not turn-based though and battles happen on the map like a Resident Evil game). I haven't gotten around to playing the PS2 sequel yet, but I hear many like it less, but I'll mention it exists and not sure the "popular word" is accurate or not.
I'm tempted to recommend more, but I'll stop there. Not on these platforms I don't know if you ever got around to playing Deadly Premonition, it's worth checking out. If you haven't played the Condemned games, you should (first one is on Steam and goes on sale regularly for like $4). Call of Cthulhu: Dark Corners of the Earth is good, but can be a bitch to get to run on modern computers. God, I said I'd write some favorites but I feel I'm barely scratching the surface here, and some of these are kinda' rough recommends but I did find them incredibly charming and think you might enjoy them.
I saw you tried to play Forbidden Siren recently. I enjoyed it, but I warn it is one tough cookie to get into. It's quite long and takes a while to figure out how the game's "logic" works for progression, but there's a lot of good moments in it. If you still have your PS3 around I'd recommend trying Siren: Blood Curse. It's not a replacement for playing the first game as it's quite different, but it's a reimagining that's more accessible and I think might be a good option to sink your teeth into (it's not nearly as cryptic or hard as the first game, but the first game is up there as sometimes one of the most cryptic and challenging horror games, so it's still fairly challenging just on a more normal type of way).
