I have come to a similar realization as I've gone through mutt early 20s. Story is the most important to me, I can suffer through bad (or non-existent) gameplay if the story is fantastic, whereas the game must be pretty good for me to play it without a story.
The House in Fata Morgana hands down. Admittedly one of the least interactive visual novels though so not really a game.
999 is very emotional and has a lot more gameplay, and stands relatively alone from the rest of its series (which is definitely worth checking out too, it's just that you don't need to in order to have a complete satisfying experience).
NieR 1 (Automata's good too, it's just more abstractly good, like more interesting to think about its themes), Last of Us 1 (2 if you have a strong stomach for deeply unsettling subject matter), MGS1-3, Mass Effect 1&2, Prince of Persia: The Sands of Time, RDR1&2 (if you can stand the clunkiness and outdated nature of Rockstar's gameplay and mission design).
Deus Ex 1, Human Revolution and Mankind Divided for deep noir Cyberpunk explorations of humanity.
I have a soft spot for Tales of Symphonia and Abyss' stories, Xenoblade 1 & 2 as well, despite all being. Bit standard anime-ish at times which some may dislike.
The Swapper is an underrated pick. Very deep and existential.
By most accounts 13 Sentinels is fantastic.
The Walking Dead Season 1 (haven't played the rest so can't vouch for it) and Tales From The Borderlands.
Halo 1-3, ODST and Reach for not super deep stories but still the best in the FPS genre.
Fire Emblem Three Houses so far is cool, just a bit too long.
Oh and of course Undertale and Deltarune Chapter 1 (episodic, only part that's out yet).
Edit: Oh yeah gotta 2nd Outer Wilds, though it's story is sort of abstract.
