I'm quite torn about Dorfromantik (a tile placement game) in this regard. The relaxing music and ambience, the beautiful graphics and the minimal interface and lack of time pressure all point to a relaxing game.

Getting a high score however -- one of the game's principal extrinsic goals -- puts my brains into a bit of a stress modus because I'm mentally rotating pieces, moving around the board, evaluating probabilities and hedging against the luck of the draw. To play optimally actually takes a lot of focus.

You can build your landscape solely based on aesthetics but unfortunately most of the game's unlockable content is gated behind milestones that can only be reached by a min-max playstyle. This is a conflict in the game's design imo.

It's worth mentioning however that the game also comes with a map editor in which you can place arbitrary tiles to create your dream landscape. You are completely free of any pressures but also can't unlock additional content in this mode.

Monster Hunter. It is so relaxing to play and has so much environmental atmosphere.

Minecraft is definitely cozy. I find assassin's creed quite cozy too

For me it’s civ (every iteration since III) and crusader kings 2 (3 isn’t quite there yet). Any game I can pause at any time, really.

But those two, man, they’re contenders for my lonely island game.

Counter Strike was my cozy game when i still played.

Celeste, despite the difficulty, the game's artstyle and storytelling was so well executed that my motivation to continue and improve crushed any frustration there possible could've been, even in the most difficult levels.

Normally I'm normally not that patient with games, so yeah, Celeste cozy af.

Not joking, although I understand it seems very silly at face value.
Dark Souls 3 PvP specifically SL60+6 at gank town (after pontiff).
It used to be my go-to wind down after a work day.
It made me smile and actually relaxed me enough to go to bed and sleep, especially after a hard day.

I personally really enjoyed Subnautica. The serene feeling of diving around while listening to found tapes, doing everything at you own speed, while learning to live in the local ecosystem.

Especially diving into the deep zones really makes me relax. Absolute darkness, only the light from your cockpit and the sounds of the beings which you cannot see. Sometimes the sound of the hull of your sub scraping against the obscure walls of the caverns. Navigating only using the way points that you set after carefully having probed the way using the smaller craft, which could not actually go the full depth.

And then I got the sonar upgrade, which kinda destroyed the vibe, so I disabled it when going deep.

Any game in easy mode. But none of these games lasts the longest without challenges, even minecraft stops being cozy when you find yourself spending all your time digging.