Isn't this pretty much the GoW fan-lore but actually canon? IIRC, this spurted out the 9 dimensional DMC incident. It's weird that Death Battle glossed over Bayonetta's cosmology. This is usually the type of geeky stuff they love to shove into our throats when they talk about DC or Marvel.
https://vsbattles.fandom.com/wiki/User_blog:Comicgyal/The_Way_to_Paradise