Just an open world survival game, only you’re a cat, dealing with regular cat problems. You have to hunt, avoid larger animals, compete with other cats, figure out which humans are dangerous and which will give you treats, judiciously spray things to maintain your territory, maybe mate and reproduce (your sex and fertility status are basically difficulty settings), etc.
You start out as a housecat going on a spring vacation with your family, and that’s the tutorial section. Then your humans accidentally leave you behind at their country vacation home, and then the difficulty is just the passing of seasons. See if you can survive winter and see your humans again next spring.
Not what you describe, but perhaps Cats and the Other Lives would catch your fancy?