I've been playing Magic The Gathering Arena since 2015 when it was in Beta. The Beta version is how I learned to play Magic. Prior to the online game, my children had tried to teach me how to play paper magic with physical cards at our dinning room table. I struggled with card verbiage.
Once I found the beta version of Magic the Gathering, I locked myself in my bedroom most evenings and played the game alone on my laptop against other players who had also found the beta version . I rarely ever won, but I was actually learning the mechanics of the game and more importantly, I was learning to understand the verbiage.
Finally, after a few weeks I felt comfortable enough to attempt building my own deck but I wanted a real deck, not a digital one. I wanted to be able to play Magic with my children. I asked them for a Deck Builder's Toolkit for my Birthday. To my surprise, they actually came through for me. My first set of Magic Cards was the Magic the Gathering 2015 Core Set Deck Builder's Toolkit. I've been playing Magic ever since, and it is my go-to cozy game! Yes, I consider deck building to meet the "farming/building" criteria of cozy games and while you are trying to deplete your opponent's life total...
Ok, maybe Magic the Gathering isn't a cozy game, but it's pretty darn close.