Logically, I think the stories were written in our world first, but then these stories somehow spawned the creation of these realms of stories, where the characters came to life with freedom of their own.
But that’s problematic too because in the case of the more classical fairytales, authorship is shaky at best. How do you deal with, say, traditions of oral storytelling? The Brothers Grimm and other folklorists who collected and adapted folktales aren’t technically their “authors” in any kind of generative sense — more like, cultural translators. And based on the show’s own mythology, the Author isn’t supposed to invent, but record. I think you have to assume the prior existence of all the realms for the show to work, but at some point it just becomes kinda nonsensical (like the multiplication of fictional Londons).