Totally get the cultural thing. That said, Story usually is important for my taste. All my favorite games ever - Metal Gear Solid, Metal Gear 3 Snake Eater, Mass Effect trilogy, Dragon Age 1 to 3 (yes even 2), The Witcher Series. God of War 2018 and 2021, Freespace 2, Tyranny (and slightly less Pillars of Eternity), spam a few genres but all have in common being story-heavy, all of them.
Hey, if you guys know other great gaming narratives, let me know.
I basically spend my life playing games, and I love sharing, so just ask

I can't promise you my recommendations will be adequate (
Ghost of Tsushima, for me, isn't really more predictable nor less story-heavy than
Mass Effect 3 for example), and it also depends if you are more interested by the quality of the plot itself, the delivery/pacing and/or the characters, but I can at least list some of them :
I was pretty impressed by the
Bioshock Infinite story (though I found the game mechanics somewhat boring). Definitely a "play mainly for the plot" game for me.
The whole
Yakuza serie is rather narrative-focused (though with tons of side activities), with pretty serious main quests and pretty goofy sidequests.
If you feel adventurous,
Spellforce 3 is a weird but rather remarkable RTS-RPG with excellent writing - the plot itself might be just above-average, but I found the characters and the execution really interesting (notice : I'm strictly speaking of
Spellforce 3 here, NOT the previous entries of the series, which were made by a different studio and have absolutely NOT the same style).
Cyberpunk 2077 is a bit of a genre-definer as a movie-like adventure with cinematics dialogues and action.
The Owlcat games (
Kingmaker,
Wrath of the Righteous and
Rogue Trader) are all typical
Baldur's Gate heirs (isometric squad-based story-heavy RPG). If you loved BG2, you are liable to love them. Notice that they are pretty sweaty in the min-max department if that's your thing.
I'm wondering if you'd like
Kingdom Come Deliverance 1 & 2. Their schtick is that they are
extremely grounded and realistic, including the main story, and focused on being authentic and detailed relative to the setting. So depending on your sensibilities, it might make them boring and pedestrian, or it might make them refreshing and original. They are gorgeous and very immersive in any case (though they suffer from a pretty clunky if interesting combat system).
And, of course, I guess you already know about
Planescape : Torment ? Pretty much the heaviest narrative-based game, like, ever (or at least close, it's often amusingly described as a video game novel), and has been among my absolute favourite since I played it.
Not really, no. Exactly because of the characteristic low-key storytelling of that genre. But as these last few years I have tried to improve my skill and prowess in mechanics, I decided to give the genre a shot. I had the original Demons Souls but never played it, so I figure the remake was a good place to start.
Regards

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Ah yeah, you won't get a strong typical story from them, that's for sure. Though what you'll get is a very strong "experience" and "indirect story" - a bit like living a myth.
I absolutely can't say if you'll like them or not, but there IS some heavy narrative in these game, but it's a "background narrative" rather than a story with a plot. It's more like "discovering the setting" through tons of hints and little bits of partial information (and reading on the Internet the fans who link all that together and offer insight you would never have had). You'll never get complete and clear answers, but it definitely gets the imagination running.
(Sekiro is a bit of an exception here, it has a comparatively clear story, but it still kinda is mostly a background event you just happen to go through and the fighting is the overwhelming majority of the reason to play it)