I'm not really sure what exactly the ambient horror genre is/entails (I'd love some more examples if you have any!) but I LOVED the Deep Sleep series and I think these games might give you the experience you're looking for - none of them get too in-your-face with the horror:
- Mouthwashing. If you're at all into psychological horror games you've probably heard of it already LOL but it really really does live up to the hype. It's the most similar to Deep Sleep out of all these in terms of gameplay - mostly a walking simulator with the occasional tense/action part.
Avoid the fangroups at all cost, but everything about the game itself - graphics, sound design, plot, presentation - is FANTASTIC. Forewarning, though: it does get really dark and it's pretty much as gorey & graphic as the low-poly style can be, so make sure to take your time with it if it's getting to you!
- Inscryption. Also a super popular one, haha... but again it's popular for a reason! It's a deckbuilder roguelike with a lot of extra mechanics and puzzles. I'd honestly say it has the best atmosphere of any horror game I've ever played. And as a bonus, the gameplay is genuinely really fun - rare for such an experience-based horror game!
- KinitoPet and Buddy Simulator 1984. They aren't connected to each other or anything, but I'm including them in the same point because they're very similar, and if you like or dislike one, you'll probably feel the same about the other. At their core, they're both interactive fiction games with the attraction based around digital fourth-wall breaks (like "referring to you by your PC account name" or "using the names of your Steam friends," stuff like that).
KinitoPet is more experience-based and Buddy Sim has more actual RPG-style gameplay. Personally, I prefer Buddy Simulator, but KinitoPet is much more popular. If you prefer gameplay over story or more subtle horror, go with Buddy Simulator; if you like having more control/interaction in the story and want to see some interesting fourth-wall-breaking mechanics, go with KinitoPet.
And some honorable mentions that I haven't played myself but I've heard are pretty good: Pathologic Classic (famously difficult psychological-survival horror, one of the defining games for the genre); Iron Lung (short & surreal exploration game, apparently very stressful); and No I'm Not a Human (dark apocalyptic-esque survival 2D RPG).
I hope you enjoy at least one of these!! And like I said if you have any ambient horror recommendations for games like Deep Sleep, you should totally let me know, the Deep Sleep trilogy is one of my favorites of all time.