Let’s start with the details of the type of game I’m looking for.
To start with, the platform doesn’t matter.
The game should be an open world type game, focused more on solving a mystery rather than on the combat.
It doesn’t have to be a complete world. Something like a city surrounded by impenetrable fog or some such is ok, as long as you get to explore all the buildings and houses individually.
Ideally it would be something you can take at your own pace rather than being forced to advance by artificial time constraints.
I played Elder Scrolls: Oblivion in the past, and that’s the closest I can think of. Are there games like that, but with more of a focus on mystery and adventure rather than combat? Other pluses would be fixing flaws like NPCs experiencing perma death if you don’t go through the game quickly enough, or not being able to go back and do some side quests if you advance the main quest too far. More detailed small scale exploration (I.e. not all the houses are the same) would be a plus.
It kind of sounds like you’re describing a survival game, like Subnautica. It’s certainly open world, there is a mystery to solve, and you can do stuff in whatever order you like, taking as long as you like. But there’s (almost) no combat, or NPCs for that matter, so it may not be the kind of thing you’re looking for.
The Witness is an open world game exploring a “strange island” in an open world setting (though you unlock access to areas as you go along). However, despite the overarching mystery, it’s mainly handled via legitimate brain-teaser puzzle minigames rather than solving clues.
The Talos Principle is a scifi mystery game played in an open world (though, again, progress unlocks parts of that world) with vaguely Portal-esque puzzles. Discover who you are, why you’re here, etc etc.
Again, while both are based around an overarching mystery, the puzzle-based problem solving might not be what you’re looking for.
It doesn’t have to have NPCs. I just mentioned them because one of the things that really bugged me about Oblivion was NPCs dying from random things things like getting eaten by a wolf or falling off a cliff, and that the higher you leveled your character, the more likely random NPC perma death seemed to occur (i.e. the wandering villager stood a better chance against a random boar than against a random mountain lion, and a better chance against the random mountain lion than against a random bear).
LA Noire somewhat fits your criteria, in that it’s a fairly open world (or rather, lovingly recreated 1940s city) and is full of (hard-boiled detective) mystery. I think it’s fairly devoid of combat, but is lacking much to do outside the main storyline - it’s been years since I played it.
Planescape: Torment comes to mind. It’s an Infinity Engine RPG based on 2nd edition AD&D, but combat is a minimal part of the game and most of the plot unfolds through dialogue. It’s set in Sigil, a city at the center of the multiverse which is home to thousands of species from countless dimensions and ruled over by the Lady of Pain, an inscrutable godlike being (but don’t dare call her a god) whose attention it’s best to avoid, because nothing good ever comes of catching it. You play an amnesiac immortal who has just awoken on a slab in a mausoleum, with a talking floating skull purporting to be your best friend and a message from your past self carved into your flesh telling you what to do if you lose your memory, and the story revolves around finding out who you are, how you ended up that way, and what you’re gonna do about it. It’s got a surprising amount of quality voice talent for a '90s game and it’s a very captivating and surreal experience.
Shadows of Doubt is an open world randomized mystery game, with a few RPG elements. There’s no supernatural evil to be found, but if you want to put on your trenchcoat, walk the rainy city streets and question suspects, dust for prints at crime scenes, do a little light burglary, and create elaborate charts with pictures and string on a bulletin board, this is the game for you.
…No Man’s Sky’s main storyline fits the bill here. Open world(s). Mystery. Do at your own pace (or you can choose not to do it at all). It is primarily a space-simulation. But you can choose how you want to play it. Some like the combat, some build bases, some, like me, just like to explore strange new worlds, seek out new life, and civilizations. But if you want to follow the storyline and discover more about the underlying mystery, you can do that too.
Try Call Of The Sea. It’s not open world in quite the way you want, but it’s a great mystery adventure about a woman looking for her husband who has been reported lost at sea.
It is described as open world but not sure it is what the OP has in mind. Still, I’d strongly recommend Disco Elysium to anyone. I think the OP might like it (not sure). There is almost no combat (and no pew pew…more like a dialog choice to punch someone).
Disco Elysium is very much a spiritual successor to the above-described Planescape: Torment, incidentally. If you enjoy one, you’ll likely enjoy the other.
I should finish Disco Elysium. It’s the weirdest thing I’ve ever played and definitely one of the coolest. It almost feels like reading a novel more than playing a game. Even though, to be clear, there are lots of choices you make. It really is an RPG. But it’s… literary.