I remember trying to play those (and failing miserably because I of how young I was). Maybe I should give them another go.
You might want to give the “The Room” series a shot. It starts out as just a digital puzzle box, but gets more involved as the series goes on and explores lovecraftian themes. There are monsters, but they’re set pieces or serve to further the story and typically only show up for a couple seconds or so in cutscenes. I personally dislike horror games, mostly because of jumpscares, and I’m completely fine with these games.
There are versions for iOS, Android, Windows, Switch and even a VR one, that is really well made. I would personally recommend the Steam versions, because they are a lot more detailed.