Change Router::with_state and impl Service for Router<()> (#1552)

* Implement `Service` for `Router<(), B>`

* wip

* wip

* fix some tests

* fix examples

* fix doc tests

* clean up docs

* changelog

* fix

* also call `with_state` when converting `MethodRouter` into a `MakeService`

* suggestions from review

axum-extra/src/extract/cookie/private.rs

@@ -68,7 +68,7 @@ use std::{convert::Infallible, fmt, marker::PhantomData};
 ///     .route("/set", post(set_secret))
 ///     .route("/get", get(get_secret))
 ///     .with_state(state);
-/// # let _: axum::routing::RouterService = app;
+/// # let _: axum::Router = app;
 /// ```
 ///
 /// If you have been using `Arc<AppState>` you cannot implement `FromRef<Arc<AppState>> for Key`.

axum-extra/src/extract/cookie/signed.rs

@@ -86,7 +86,7 @@ use std::{convert::Infallible, fmt, marker::PhantomData};
 ///     .route("/sessions", post(create_session))
 ///     .route("/me", get(me))
 ///     .with_state(state);
-/// # let _: axum::routing::RouterService = app;
+/// # let _: axum::Router = app;
 /// ```
 /// If you have been using `Arc<AppState>` you cannot implement `FromRef<Arc<AppState>> for Key`.
 /// You can use a new type instead: