Oceanhorn
Puddle

I remember falling asleep on the keyboard every time I tried playing Banner Saga though.

Stacking

One of the Shantae games, perhaps? Pirates Curse is often (rightfully) considered the best of the series, but Risky's Revenge is also well worth playing and provides context that makes Pirate's Curse even better. Both are very colorful and lighthearted games with great music and oodles of personality.

I'd suggest Triple Town or Unholy Heights.

If you're more strategic-minded but want something cozier, The Settlers II/III/IV might be worth a try.

Banished.

Settlers 2.

Huh, I would never have said Race the Sun is relaxing or anywhere even near that. It's a race game where you a) die if you don't keep up with the sun setting on the horizon, b) die if you crash into any of the myriad obstacles that pop up in your path. I suppose if you were just ok with crashing into the same obstacle repeatedly as some sort of zen-y simile about accepting the grind of life...maybe?

I was going to say Glass Masquerade. Beautiful and super relaxing despite the challenge. But not on GOG. And very short, if replayable for those who like puzzles.

Seconded.

I find myself installing mods though. I started with these:

https://www.youtube.com/watch?v=5M-21h5z7nM

I need to find a Saved Game mod as well. I keep getting interrupted when I'm playing.

First of all, Ghost Of A Tale is scary as fuck at the start.
Thus, I recommend Fran Bow, which is also not the game it seems to be when you start.

There's the Sunrise DLC, which is a zen mode for Race the Sun.

Which reminds me, Zen Bound is a great game for this sort of thread.

There is an open drive mode in Mafia. but that ,might be too relaxing. Let's face it, when you aren't being shot at, chased, or chasing, New Haven is kind of boring. :P

And another shout out for Stardew.

And I don't know why Kerbal doesn't get more love for being relaxing. The career mode can be a pain, but the sandbox stuff is great because you have nothing to lose. If you crash and burn, try again, no big deal. You can just sit back and let your imagination run wild. Of course, if you manage to get a good orbit going, turn up the music, turn off the lights, and watch the planet roll by peacefully beneath you.

TRI: Of friendship and madness
RimWorld
Factorio
AER Memories if old
Grow Home / Grow Up
Qbeh-1: The atlas cube
The Talos principle

If browser games are acceptable, and you're interested in a game you can just leave running while doing something else (and still progress in the game), you might look into Cookie Clicker or similar games.

Also, I remember that you could just leave the original SimCity running and still have your town grow. (Is this workable in the sequels?)

Edit: Another idea I thought of. Try Morrowind, and just focus on exploring the world; you don't have to do quests if you don't want to.

If none of the above suits you, then you should try this!