All fiction is fanfiction
You knooooow I will get on this soapbox all day long. All fiction is fanfiction. All art is fan art.
Long before we had the (very super recent modern) idea that a book = a discrete, permanent object, we had collective folk texts that spread precisely because people remixed and remade them.
There could be no such thing as faithful reproduction. All transmission is recreation. The Iliad began as oral literature; Virgil borrowed a minor character and made him a hero of Rome in the Aeneid; Dante borrows Virgil and makes him his guide to purgatory in the Divine Comedy. Writing that builds on the universe of other writing is among our oldest forms of storytelling.1
I like this definition of fanfic: the communal rewriting of a source text in conversation with each other.