Pastiche

A pastiche is "a work of visual art, literature, theatre, music, or architecture that imitates the style or character of the work of one or more other artists." The dividing line from parody is intent: "Unlike parody, pastiche pays homage to the work it imitates, rather than mocking it," and the article describes the modern pastiche as "a deliberate, witty homage or playful imitation." The shelf is long: Sherlock Holmes stories continued by other hands after Conan Doyle, David Lodge's 1965 novel as "a pastiche of works by Joyce, Kafka, and Virginia Woolf," and Banville's Mrs. Osmond (2017), written close to Henry James's style.

For the writer pastiche is style study made public: imitating a voice closely enough to honor it is also how a writer's voice gets trained. Fan communities practice it constantly, and a pastiche played for laughs crosses the border into parody.