[FastAPI docs for `lifespan`](https://fastapi.tiangolo.com/advanced/events/).
                """
            ),
        ] = None,
        # the generic to Lifespan[AppType] is the type of the top level application
        # which the router cannot know statically, so we use typing.Any
        lifespan: Annotated[
            Optional[Lifespan[Any]],
            Doc(
                """