Life is Strange made me cry. It has a good soundtrack too.

The first walking dead game from telltale was good, but if you've played anything they've done its largely the same.

Papers please can get emotional, but it's mostly intense pressure.

I haven't played it myself, but I've seen playthroughs of The Last of Us. Even though there's a sequel, I've heard the first one is better. Anyway, if engaging story is what you're after, I'd check that out.

I've also never played this one, but I've heard SpecOps: The Line is also a gutpunch.

It's a bit of a commitment, but I always found the Halo series to be kinda emotional to me, but then I also grew up with it and got invested in the characters. Your mileage may vary with Halo.

Final recommendation would be Ori and the Blind Forest if you're into platformers.

Haven't seen Spiritfarer mentioned, worth checking out.

I thought Ori and the blind Forest was rife with emotion

I'm not super familiar with the examples you gave but I'm gonna say anything from Supergiant Games: Bastion, Transistor, Pyre, Hades. Fantastic music always, I would say the storytelling is done best in Transistor and Hades.

Brothers a tale of two sons.

It is very emotional

Mass effect and dragon age series from bioware are excellent, they're a little involved but the story telling is incredible in both. While it has aged and may be depending on a love for star wars, their knights of the old republic series was also excellent.

They're really damn good at making a story that's worth being part of, often one of my first recommendations aside from the last of us, outer wilds, and a couple of others I've seen here already.

Bastion has a good story and great OST. There's a pretty heavy moment toward the end of the game.

🎵I'm coming home, sweet home🎵

I just finished OneShot this week and I think it could be what you're looking for. It certainly would if you play the whole game.

You can get very personally attached to the characters in a way that I've not had in a game before. It was very hard to finish the game amongst all the tears.

Since you’re ok with horror, I highly recommend both Detention and Devotion by Red Candle Games. Both of them start out as horror, then gut punch you as you realize what’s going on. Devotion is an amazing example of domestic horror (the horror that can happen inside the home), and Detention is the horror that people do when they don’t realize the consequences of their actions. Devotion has stuck with me, and to this day the last line makes me want to cry.

Maybe What Remains of Edith Finch? Also, maybe it was just a weird time in my life, but I think I bawled hardest at the end of FFVII: Crisis Core back in the PSP days. Braid is an emotionally weird one as well.

This War of Mine

Gris

Death Stranding had me all over the place. Also the first season of Telltales The Walking Dead.

Basically anything with kids can set me off and I find somewhat difficult nowadays as I have children of my own.

Final Fantasy X still holds my personal ugly-cry record. To this day, I can't hear some of the music from it without tearing up. It's one of those games that has emotional react videos on YouTube.

Shadow of the Colossus manages to be emotional with very little explicit story. A lot of it has to do with its use of dynamic music in an orchestral soundtrack.

Persona 3 just had a remake, and that's part of a series that can really gets its hooks into you. A big part of it is the parasocial gameplay, but even if you're not the type to get into that, the story is still very moving. Persona series composer Shoji Meguro recently said the ending theme in this game was his magnum opus.

My recommendation would be RiME and Spiritfarer, both managed to make me cry.
Spiritfarer talk quite a bit about death, sometime through diseases (cancer, demencia, etc.), but in a different way than To The Moon, and you may find it ok.
RiME topic is a bit different, but cannot be spoiled unless you want to diminish the impact. In my case I went blind and damn it hit me like a truck 😅.
On the stellar OST side you could try Gris. Pretty emotional too, but in a way more abstract way than the first two.
On the topic of war and its horrors you got Torn Away, as well as This War Of Mine, both very emotional journey.

It's a long game, but Xenoblade Chronicles 3 messed me up in all the right ways. Especially if music moves you, I recommend it. Mostly standalone too, if you didn't play the other 2 main games.

This game has very powerful moments.

I really wanted to suggest Nier Replicant, but, seeing as you didn't like Automata, I guess there's no point. I enjoyed both, though, since I kind of was in a specific headspace the time I played them. I also took both at face value initially, which has helped

Other than that, may I suggest Beacon Pines? It's all about the story, so I think you'll love it. The way you discover different branching paths the story takes is also quite novel.

I also loved FAR: Lone Sails. It's more of a "show, don't tell" kinda story

There's also this itchio game I found once -- Under a star called Sun. It's super short, though

The Witcher 3 has some really emotional scenes, and an immersive soundtrack.

I know it has a bit of an intense fan base, but Undertale would definitely fit here.

I would wholeheartedly recommend the A Plague Tale duology (Innocence and Requiem). They both had a lasting impact on me (especially Requiem) and the overall presentation is really great IMO.

I found "Journey" to be very emotional at the end. Also, although it's real slow and not everyone's cup of tea, "Everybody's Gone To The Rapture"

To the Moon was great. It's made with RPG Maker and it shows, but it hits hard.

Xenoblade Chronicles 1-3 & X

@seliaste
I just finished Enderal (Skyrim Total Conversion mod). That left me crying at the end (and one quest in between as well)

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

Brothers: A tale of two sons.

Only game that ever made me cry alone.

Rage and anger are emotions so I'd suggest League of Legends

If it's emotional you want, you can't beat To the Moon and its sequel, Finding Paradise. They're walking sims, but they've got great stories that'll make you ugly cry

Several games I'd have recommended have already been said, so I'll chuck in a nod for Thomas Was Alone, incredibly moving despite the only 'characters' being a range of shapes.

The Talos Principle, despite being a puzzle game, has a gorgeous story if you take your time to listen to the audiologs and read the files you find in the world.

Iconoclast is an action platformer with great story and characters. It takes a bit to become interesting imo, but it grew on me the more I played it and I remember it fondly.

Signalis is a survival horror game that combines a presentation similar to that of old school Resident Evil games with lovecraftian cosmic horror. The story is very cryptic and requires a bit of effort on the player's part, but I really enjoyed it both for its themes and the characters (more than the actual gameplay).

A Plague Tale Innocence/Requiem are two action adventure games with an enthralling story, well written characters and a gut punching ending. The disease aspect of the story is not prominent in the first game, and the ending is satisfying imo, so you could stop there if diseases are a no-go for you.

I really liked Life is Strange 2 and its themes really resonated with me, but it is very divisive among fans.

I also enjoyed Haven's sci-fi love story, and found it one of the best depictions of an actual relationship in gaming: where most games tend to end when two characters declare their love/share a kiss/whatever, Haven's beginning is well after they got together and the entire game is them being together, talking and joking and stuff. If you're a bit sentimental, you may like it.

These are just games from the current/last gen, but you can find other great stories if you are willing to play with an emulator or have old consoles lying around. Xenogears is a JRPG from the old PS1 days, and it's still the best one of its genre. Oddworld Abe's Oddysee is a puzzle platformer with very modern themes despite its age, and its mix of fairy tale-like storytelling and horror/splatter presentation is very unique and engaging. I still think of Rue's story in Threads of Fate as one of the most emotional stories I've played as a kid.

I could go on, but I already listed waaay too many titles lol

You might like Inmost.

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.