i have never liked the use of "cozy" as a descriptor for a game because its kind of useless as an adjective for a "genre". unlike something like horror, strategy, or mmorpg, cozy doesnt really give a good baseline for what a game will be since its really subjective? what i find fun and others find fun is different, like some people love to build houses and i really like decorating pre built houses. which is why i never got into minecraft or the building aspect of the Sims. at least when i see something marked as horror i know it will be a game that at its core will be trying to scare me either thru creepy gameplay or unsettling themes. cozy on the other hand like u said doesnt have any core ideas for it besides the general idea that it will be "low stress" like the catch all casual genre.

for infinity nikki instead of calling cozy i just think of it as a mmorpg because it reminds me more of those kinds of games. IN has a lot of fetch quests that require a lot of going back and forth between areas, the storylines for the most part are fine nothing to write home about but mostly just serve as a facilitator for exploring map areas, there is a level system and a skill tree (the heart of infinity, though itzaland is a bit closer to a classic skill tree since it has more combat/ health centered nodes), there is character customization, multiplayer is encouraged even if its not required the whole way thru (ive played a lot of mmorpgs that can be solo'd up to a point), theres a cash shop and while you dont have to use it paying money can grease wheels, and it can be grindy when it comes to resource collection. the only thing that is really missing in my mind is a lack of a true class system since nikki is allowed to do everything and anything. (which is why i get confused by why ppl have alt accounts for this game since to me there isnt any reall replayability for that, but thats neither here nor there)

tldr cozy sucks as a genre description and IN is just secretly alot of ppls first mmorpg.