You might like Inmost.

Kattawa Shoujo.

Drops mic

I'd recommend "in stars and time". It is a turn-based RPG with loveable characters. I think it is best played blind so I'm hesitant to tell you more, but if you like games like undertale then I think you would like it.

I'm surprised no one mentioned it. Hellblade (full title: Hellblade: Senua's Sacrifice) had me in literal tears. Not only it's a decent game, it's also an essay on heavy topics like mental health and the story of viking invasions.

Stray!

The LISA games.

Undertale and Deltarune are easy recs, emotional and fun to dig into the lore and details. Deltarune in particular is an ongoing series, so there's lots of speculation and theory crafting if that's your thing. Amazing soundtrack as well. Undertale should be played first, though. Deltarune isn't necessarily a sequel, but Undertale gives some context to certain things. Both are best played blind.

Inscryption is a really fun deck builder with a very intriguing story and some surprising twists and turns. Even if you're not much into deck builders, the game is structured such that it's pretty much impossible not to get a winning deck over repeated runs. The atmosphere is also top notch.

Ghost Trick: Phantom Detective isn't on steam, but it's definitely worth a buy on one of its supported systems if you have them. Great puzzle game with a lot of humor and mystery. Not quite as emotional, but very strong characters and an ongoing mystery that kept me invested.

Oxenfree is a really intriguing mystery game with some horror elements and a great soundtrack (I originally checked it out after hearing Beacon Beach and loving it). Overall the game really scratched the itch of that feeling of reading horror stories before bed.

There's also a free, short Silent Hill game on PS5 called The Short Message. It has mixed reviews, but my friends and I found it surprisingly engaging. At first it seems pretty on the nose with its message, but things get a little deeper as you go on. Aside from some cartoonishly evil characters and a somewhat frustrating final sequence, it's worth a look.

Baldurs Gate 3.

Before Your Eyes

Borderlands 2, then the expansion Tiny Tina's assault on dragon keep.

The last of us 1 and then 2. There are video games and then there's TLoU p1&2. If you can, play 1 on pc. The controls aren't great in 1 (IMHO) but kb&m made that so much better. P2 they made the controls much better. It's a more fun game to play in my experience with less frustrating sections, and whilst people prefer 1 or flat out don't like 2, I think the drivers for that aren't to do with the story or game not being good, in fact, I would say p2 is the best story driven game I've ever played (better than rdr2 which I loved and is another one you should consider, 1 and 2 actually). People will just not like 1 specific thing or another (there are lots of small things in the game that certain people will have issue with, you'll understand when you play it) and then because of that 1 thing say the whole thing is bad. People that complain are often louder than those who praise.

I am into emotional storytelling as well, I think what gets you involved most are well drawn characters.

I would recommend planescape torment for an epic adventure full of stories, characters and heartbreak.

Really good stories/characters are few and far between in computer games but "The longest journey" comes to mind and even the first Witcher game.

Unavowed comes to mind as well as a rather affecting story.

And a couple of dozen books, but that's not what you asked for...

The Stillness of the Wind is a short, peaceful, beautifully scored farming game that will fuck you right up. Have a huggable blåhaj nearby.

Mother series. especially Earthbound (Mother 2) and Mother 3