I think its how you go about things rather than specific things like removing combat or death which I really dont think are anathama to cozyness at all. For example, the dying Earth Books by Jack vance are peak cozy, and they are modestly bloody and have a decent amount of combat.
And I think thats primarily because of how he describes and portrays things. he talks very vividly about how things feel and seem, and it gives the world a sense of whimsy and appreciating for the little things. not even necissarily the little GOOD things, just the underlying nature of things. A fascination with life and experience in a more raw and primal form. Like one of the short stories follow an atempted rapist trying to bed a beautiful forest witch, and instead of painting him as primarily bad in a moral sense (which it definetly implies) the main aspect of his character is a great passionateness, giving of a dashing rogue figure. It talks about his great lively golden eyes, and his hearty swagger. He eventually does get his comeuppance, but that is not something that attempts to take away from his panache.
Its about vivedness, and not vivedness to any particular ends, but a vivedness that attempts to get at the sublime and greater weight of anything. The bread that you buy has signifigance. the stars that you observe have signifigance. If you are skimming over things to get to a more utilitarian point, thats where cozyness ends. when you focus too much on quantitively and not enough qualitivity.