When the focus audience of a piece of literature is the writer, the purpose of the piece is?

It's not informative since that would be talking about a specific topic that you're supposed to come to a realization, it's not entertaining since it's not a story driven piece, persuasive it isn't because if it's about the writer then you aren't learning anything about a specific topic, so that leaves expressive. It is expressive since the writer is talking about themselves