The first game I ever played of the genre was probably Wandering Willows. It’s quite old, release was in 2009. It was very different from all the other games I played up until then (which was mostly Final Fantasy, Zelda, Mortal Combat and the like xD).
You are stranded on an island and have to fulfill quests and help the villagers. As a companion you can catch various pets and level them. There is also farming and character customization.
Harvest Moon 64! I still go back to it every few years.
For me, it was the original Harvest Moon, for the SNES.
Stardew Valley
i’m not sure if it qualifies, but i found minecraft classic quite wholesome.
Back in 2010 there was Minecraft 0.30 as a creative mode available free to play. People used to build houses with flowers as water tap. Good times of just placing blocks.
My first cozy games were Animal Crossing on the GameCube and Harvest Moon it’s a wonderful life on GameCube. I fell in love with both games and played them endlessly.
Loved that game, so cute!
The Ranch of Rivershine, which released this year. Yep, and I am not ashamed (maybe a bit). We always pre-play the games our daughter gets a bit and with this one I just couldn’t stop. Not at all what I normally play. I hope they add more content soon.
Probably Animal Crossing: Let’s Go to the City which my parents bought me around 2011 I think? I loved the idea of decorating my house and being a nice neighbour and planting nice flowers everywhere. My favourite memory about the game was a musician who would come to the town on Saturday at 20:00(?). My cousins and I often chilled together with the game’s music running in the background ^^
harvest moon!