Mine are following:

Serious Sam
Painkiller
Torchlight
Titan Quest
Prince of Persia 2008
Brothers
Portal
Limbo
World of Goo
Deponia series
Gunpoint
Deadbolt
Contraption Maker
Broforce
Angry Birds series
Pixel Junk series
Anomaly series
Plants vs. Zombies
Orcs Must Die!



Also, there's nothing wrong in using a guide/trainer/cheat if it makes a game enjoyable/less frustrating for you.
amen to that.

I used autohotkey script to cross floor traps level in Legend of Grimrock.

A good point--and roguelikes in particular might be a poor choice.

Another suggestion: visual novels. While one might consider getting an undesired ending to be a loss state, which might then generate frustration, if approached from a direction of "seeing what ending you get" such games might work.

Otherwise, the suggestion that others have made of using cheats might be a good one: that way you might be able to get the fun of the action-elements without the frustration of being killed.

Or perhaps the gentler sort of exploration games--things like Firewatch, or A Short Hike. These provide things to do, without much real danger.

Stardew Valley.

Could it be that someone important mocked you for losing or punished for faults so now you're suffering from the fallout of that?

Anyway, two suggestions. Try the "relaxing" tag on steam for less demanding type of games. And in any other game that has difficulty setting try selecting the easiest mode.

Might I suggest Tyrian 2000? You can easily breeze though it.

Also, Knytt & Knytt Stories are all quite relaxing.

Mine are following:
AI War 2
Distant Worlds: Universe
Eschalon: Book I
Kynseed
Prison Architect
Reus
Slay the Spire
SPORE
The Incredible Machine 3

BTW, I would suggest you to give Chi Kung / Tai Chi class a try for your anger issues. The practice of Chi Kung helps manage the stress, anger, depression, morbid thoughts, and general confusion that prey on your mind. By the way, you need to do your research before you take the class you like.

Glass Masquerade are fantastic, relaxing games... Yet to come on GOG though, sorry about that!

Oh I was just thinking of things where you don't control what happens - movies, music, TV, YouTube, similar...

If you're willing to include browser games, maybe something like Cookie Clicker (or some other idle clicker)?

Alternatively, look into simulations like the SimCity series, or perhaps something like a puzzle game with a Zen mode (some versions of Bejeweled apparently have such a mode).

(Unfortunately, can't think of anything here on GOG that would be either an idle clicker or a puzzle game with a Zen mode.)

Race the Sun's Sunrise DLC has a no challenge, no frustration purpose. They even bill it as a "zen-like" mode.

But it's not puzzles or anything that really requires much thought beyond starting up and letting it run. It's a bit more interactive than say, Mountain, but Mountain isn't sold here on GOG.

Heh, book of unwritten tales is suppose to be particularly funny. Though maybe avoid Critter Chronicles...

Compared to sonic and mario, a pretty easy and extremely fun platformer is:
https://www.gog.com/game/rayman_origins

Story heavy RPGs on easy setting or point and click adventure games.

Stardew Valley maybe. You can use this mod to slow down time a bit. Makes it more relaxing.

https://www.nexusmods.com/stardewvalley/mods/169