Make AWS middleware example match real impl

The real AWS middleware in `aws-inlineable` has changed, but the example
hasn't changed to follow suit.

Author: Jon Gjengset

codegen/src/main/kotlin/software/amazon/smithy/rust/codegen/smithy/generators/client/FluentClientDecorator.kt

@@ -184,37 +184,77 @@ class GenericFluentClient(codegenContext: CodegenContext) : FluentClientCustomiz
                     // Ignored as otherwise we'd need to pull in all these dev-dependencies.
                     /// ```rust,ignore
                     /// use aws_endpoint::AwsEndpointStage;
+                    /// use aws_http::auth::CredentialsStage;
+                    /// use aws_http::recursion_detection::RecursionDetectionStage;
                     /// use aws_http::user_agent::UserAgentStage;
                     /// use aws_sig_auth::middleware::SigV4SigningStage;
                     /// use aws_sig_auth::signer::SigV4Signer;
-                    /// use aws_smithy_http_tower::map_request::MapRequestLayer;
-                    /// use tower::layer::util::Stack;
+                    /// use aws_smithy_client::retry::Config as RetryConfig;
+                    /// use aws_smithy_http_tower::map_request::{AsyncMapRequestLayer, MapRequestLayer};
+                    /// use std::fmt::Debug;
+                    /// use tower::layer::util::{Identity, Stack};
                     /// use tower::ServiceBuilder;
                     ///
-                    /// type AwsMiddlewareStack =
-                    ///     Stack<MapRequestLayer<SigV4SigningStage>,
-                    ///         Stack<MapRequestLayer<UserAgentStage>,
-                    ///             MapRequestLayer<AwsEndpointStage>>>,
+                    /// type AwsMiddlewareStack = Stack<
+                    ///     MapRequestLayer<RecursionDetectionStage>,
+                    ///     Stack<
+                    ///         MapRequestLayer<SigV4SigningStage>,
+                    ///         Stack<
+                    ///             AsyncMapRequestLayer<CredentialsStage>,
+                    ///             Stack<
+                    ///                 MapRequestLayer<UserAgentStage>,
+                    ///                 Stack<MapRequestLayer<AwsEndpointStage>, Identity>,
+                    ///             >,
+                    ///         >,
+                    ///     >,
+                    /// >;
                     ///
-                    /// ##[derive(Debug, Default)]
+                    /// /// AWS Middleware Stack
+                    /// ///
+                    /// /// This implements the middleware stack for this service. It will:
+                    /// /// 1. Load credentials asynchronously into the property bag
+                    /// /// 2. Sign the request with SigV4
+                    /// /// 3. Resolve an Endpoint for the request
+                    /// /// 4. Add a user agent to the request
+                    /// #[derive(Debug, Default, Clone)]
+                    /// #[non_exhaustive]
                     /// pub struct AwsMiddleware;
+                    ///
+                    /// impl AwsMiddleware {
+                    ///     /// Create a new `AwsMiddleware` stack
+                    ///     ///
+                    ///     /// Note: `AwsMiddleware` holds no state.
+                    ///     pub fn new() -> Self {
+                    ///         AwsMiddleware::default()
+                    ///     }
+                    /// }
+                    ///
+                    /// // define the middleware stack in a non-generic location to reduce code bloat.
+                    /// fn base() -> ServiceBuilder<AwsMiddlewareStack> {
+                    ///     let credential_provider = AsyncMapRequestLayer::for_mapper(CredentialsStage::new());
+                    ///     let signer = MapRequestLayer::for_mapper(SigV4SigningStage::new(SigV4Signer::new()));
+                    ///     let endpoint_resolver = MapRequestLayer::for_mapper(AwsEndpointStage);
+                    ///     let user_agent = MapRequestLayer::for_mapper(UserAgentStage::new());
+                    ///     let recursion_detection = MapRequestLayer::for_mapper(RecursionDetectionStage::new());
+                    ///     // These layers can be considered as occurring in order, that is:
+                    ///     // 1. Resolve an endpoint
+                    ///     // 2. Add a user agent
+                    ///     // 3. Acquire credentials
+                    ///     // 4. Sign with credentials
+                    ///     // (5. Dispatch over the wire)
+                    ///     ServiceBuilder::new()
+                    ///         .layer(endpoint_resolver)
+                    ///         .layer(user_agent)
+                    ///         .layer(credential_provider)
+                    ///         .layer(signer)
+                    ///         .layer(recursion_detection)
+                    /// }
+                    ///
                     /// impl<S> tower::Layer<S> for AwsMiddleware {
                     ///     type Service = <AwsMiddlewareStack as tower::Layer<S>>::Service;
                     ///
                     ///     fn layer(&self, inner: S) -> Self::Service {
-                    ///         let signer = MapRequestLayer::for_mapper(SigV4SigningStage::new(SigV4Signer::new())); _signer: MapRequestLaye
-                    ///         let endpoint_resolver = MapRequestLayer::for_mapper(AwsEndpointStage); _endpoint_resolver: MapRequestLayer<Aw
-                    ///         let user_agent = MapRequestLayer::for_mapper(UserAgentStage::new()); _user_agent: MapRequestLayer<UserAgentSt
-                    ///         // These layers can be considered as occurring in order, that is:
-                    ///         // 1. Resolve an endpoint
-                    ///         // 2. Add a user agent
-                    ///         // 3. Sign
-                    ///         // (4. Dispatch over the wire)
-                    ///         ServiceBuilder::new() _ServiceBuilder<Identity>
-                    ///             .layer(endpoint_resolver) _ServiceBuilder<Stack<MapRequestLayer<_>, _>>
-                    ///             .layer(user_agent) _ServiceBuilder<Stack<MapRequestLayer<_>, _>>
-                    ///             .layer(signer) _ServiceBuilder<Stack<MapRequestLayer<_>, _>>
-                    ///             .service(inner)
+                    ///         base().service(inner)
                     ///     }
                     /// }
                     /// ```