Perhaps RPG's with a party, like Mass Effect, Baldurs Gate 3, Fallout New Vegas (many companions with their own stories to find and tag along), Star Wars: knights of the old republic, dragon age.

Some shooters like the later Band of Brothers games, valkyria chronicles or the Mafia series you may enjoy as well.

In Indiana Jones and The Fate of Atlantis, there are multiple paths to choose to complete the game, and one option is to choose a fun companion come with you to help you throughout.

Bioshock Infinite - Elizabeth as a constant companion is a big theme in the game.

Beyond Good and Evil - A lot of great supporting cast like Pey'j.

Baldur's Gate 3 - Massive emphasis on the relationships you have with your companions.

Brutal Legend - A quasi-RTS where caring for your bandmates and roadies is the only way to win.

Disco Elysium - Kim Kitsuragi, enough said.

Firewatch - Story driven rooted in character relationships, about being alone but trying to stay connected.

Hi-Fi Rush - Great cast of characters who are heavily involved with story and often around or talking to you.

Just Cause 3 - Probably the best in the series, for threading the comedy/action needle and giving you characters that are really lovable.

Katamari Damacy - Feel the love of the King of All Cosmos!

Life is Strange - Rooted entirely around your relationships with close friends and classmates.

Mad Max - Your own personal Gollum!

Nier Automata - You'll always have your PODs.

Portal 2 - Wheatley will keep you good company.

Psychonauts / Psychonauts 2 - How can you be lonely when you're inside someone else's mind?

SkateBIRD - Make friends with birds!

Terraria - There's always some new villager to find.

Stardew Valley

I guess you're looking to spend time with interesting characters.

Endearing party of playable characters:

• Bug Fables — A big tiny adventure of three cute insects, with Paper Mario-inspired turn-based combat
• Cassette Beasts — Creature-collecting with heart. You bring one of several interesting companions with you.
• Moonlight Pulse — A metroidvania set on a planet-sized creature. You play as a team of planet-creature denizens fighting off a parasite infestation.

Encountering interesting NPCs:

• A Short Hike — A very small but dense open world game. You encounter characters on your way to find a cell signal in a remote mountain park. With no quest tracker or minimap, you just wander and do what you want.
• Inscryption — Card game with an immersive, spooky atmosphere. The game is hiding secrets from you, though, and you'll meet plenty of shady characters before you can get the truth.
• CrossCode — Action RPG set in a fictional VR MMO of the distant future. You wake up as a player character with no memories of real life, unable to log out. You quickly make friends, go do MMO stuff together and get to the bottom of why you're stuck in-game.

Parasocial weirdness:

• Hypnospace Outlaw — You are a janitor on a Geocities-like service in a simulated 1999 internet. You learn about all the users through their personal websites. This game expresses a large emotional range with just website updates (or the lack of them).

Golden Sun.

The most memorable RPG I've ever played. The music and art style, beautiful. Especially considering it's a Gameboy Advance game.

Persona series, maybe. The entire franchise is all about making friends, deepening relationships, and working together to fight monsters.

I saw somebody here recommend Kenshi, so I'm going to recommend RimWorld as well. It's a colony building game, but it's kind of anxiety-inducing lol

Give a try to conversational games like VA 11 hall-A and coffee talk

Divinity: Original Sin 1 / 2 Dragon Age (any) Baldur's Gate (any)

Excellent, LONG story if you want them to be. You have a group to adventure with.

Titanfall 2: You have a titan as a companion for most of the game (there are segments where you're on your own though). And it's a fantastic single player campaign.

Baldurs gate 3

All party crpg like pillars of eternity, Baldur's Gate, and the like.

JRPG maybe...

in cyberpunk 2077 your characters sorta never alone after a certain point.

Undertale gives you the option of being kind to nearly everyone you meet, and you can befriend several characters as well.

So I'm not sure what might make you not feel lonely or anxious. Things like how directly you control the characters with you could he factors I imagine, so I'm just going to list a bunch of things:

A shorter one, but Star Wars Republic Commando. You're a commando unit and work as one.

Dragon's Dogma, either Dark Arisen or the new sequel.

Mass Effect series.

I don't know if Earth Defence Force would be like that or not, at the end of the day your NPC allies could be hit or miss (literally, depending on the weapons you use).

Not sure how you feel about party-based RPGs, but there are tons of them.

I'm wondering if RTS games with campaigns would feel right as well. StarCraft's campaigns have a lot of people constantly talk to/around you.

The Lego games?

Stardew Valley?

Can't really think of indie games at the moment.

Games I haven't played so I don't know if they apply: Persona? Space Marine games?

CrossCode. Friendship is kinda part of the story / concept in a way.

You could try a Persona Game (or the new Metaphor) These games are build on your relationships with the other characters. They think of you, they contact you often on their own because they want to do something with you. You just have to like to read. Those things are half JRPG, half Visual Novel.

Midnight Suns is perfect for you. It’s part team tactical deck building combat, part superhero relationship simulator. You alternate between fighting evil as part of a squad of heroes (the DLC includes Deadpool) and spending time hanging out and talking with other heroes. And it’s just a phenomenal game all around.

Edit: OP, you okay?

Mass Effect series.

Dragon's Dogma is pretty good at making you both the center of the world and being surrounded by people that want you to succeed with how the pawns constantly talk, and even out in the middle of nowhere, you'll run into people just walking around between settlements so the world never feels empty, even in places it maybe should.

Echo

Have you tried Adastra? That story can make you feel pretty good... Until it ends...

DO NOT play shadow of the colossus... Not a big gamer but never felt so alone in a game...

Ys VIII: Lacrimosa of Dana. You will work together with an increasing team of friends and allies to survive ridiculous circumstances.

The story is incredible, but the character building is excellent. Great fast paces action RPG with party switching, so you'll always have 2 playing with you. The story really shows deep friendship development, especially if you ensure to do all side quests and talk to characters at various story points.

Baldurs Gate 3, Mass effects

I like a lot of singleplayer games, but I also play games that can be played multiplayer (open world survival crafting games).

Borderlands is pretty good imo. You can play alone, but you never really feel alone with all the characters constantly asking you to do stuff for them.

Someone else said Kenshi, which is strictly singleplayer but you can build up your party and have multiple squads running around, taking care of things. And there are generated conversations between them. And there's tons of mods that can change or add things to the game; personally I've added a couple new subraces to the vanilla ones, a couple new whole races of characters to play with, new building and weapon types and such.

Edit: Untitled Goose Game and Thank Goodness You're Here, or even any cozy game really.

The new Star Wars: Jedi games like Fallen Order and Survivor are great singleplayer games without making you feel alone. Mostly cause of BD-1.

Have you played RDR2? It's open-world, the world is stunning (you can easily ignore the stories and just take in the nature), and the game revolves around your camp/gang, which you regularly return to and interact/check-in with, in addition to accompanying them on missions at times.

Hogwarts Legacy if you enjoyed the old Harry Potter games.

Literally any JRPG

You are never technically alone in Hellblade...

In all honesty, I think you'd love Casette Beasts, it's all about friendship.

Any of the Dragon Age games.

untitled goose game.

RPGs come immediately to mind. Your partner in Disco Elysium is more competent than the main character for reasons that will be immediately obvious. Bethesda's RPGs are also open world, and while you'll start out alone in them, you get permanent companions pretty quick (especially if you know where to look). They also get more chatty in the world and more character development in the later games. Fallout 4 more so than Skyrim more so than Fallout 3, for example. Starfield makes you swap them out if you do the main story, which I don't know if you'll like or not.

For a dedicated shooter, I think Titanfall 2 has the most protective companion I've seen in the genre. Get this one on sale, since it has its robust multiplayer priced in, but it has an excellent--if a bit short--single-player campaign.

Cult of the lamb - build a cult?
Sky - a cutesy online exploration game that pppl team up in. I know it's not single-player - but it's kinda singlemulti?

Kenshi.

The world is brutal, but its possible to pay for some company, buy some slaves, or maybe, juuuuust maybe, find a quirky friend.

"Binary Domain" is an option. You are almost all the time accompanied by 1-3 NPCs of your Team. The game also has a, more or less working, voice System to talk to your team through your microphone. That way you can give orders and have some small talk. The game is quite good, give it a try.