I also don't think I can hammer down what cozy games are, I just know I like or am interested in a lot of the games that attract that label. I tend to not find time management stressful at all which is why I personally see Stardew Valley as cozy. Meanwhile, I haven't played anything in the Persona series but the aesthetics I get from the screenshots I have seen make me personally find Persona to not be cozy at all.
There was a thread awhile back attempting to start a discussion about what exactly a cozy game is that you might be interested in!