Refactor HTTP client construction and request execution (#57575)

## What changed

Construct the direct transport explicitly in `HttpClient::new` and reuse `without_request_logging` in `new_without_request_logging`.

Bind awaited request results before matching them in transport execution and the Windows proxy retry path.

GitOrigin-RevId: 58b2524491db80ff4d7a954868c1e030a1643a9d

codex-rs/http-client/src/client.rs

@@ -50,12 +50,18 @@ impl std::fmt::Debug for TransportClient {
 
 impl HttpClient {
     pub fn new(inner: reqwest::Client) -> Self {
-        Self::from_parts(inner, RequestLogging::Enabled, HeaderMap::new())
+        Self {
+            backend: HttpClientBackend::Direct(TransportClient {
+                inner,
+                request_logging: RequestLogging::Enabled,
+                default_headers: Arc::new(HeaderMap::new()),
+            }),
+        }
     }
 
     /// Suppresses diagnostics for endpoints whose URLs or headers may contain credentials.
     pub fn new_without_request_logging(inner: reqwest::Client) -> Self {
-        Self::from_parts(inner, RequestLogging::Disabled, HeaderMap::new())
+        Self::new(inner).without_request_logging()
     }
 
     /// Suppresses URL and response-header diagnostics while preserving this client's routing.
@@ -148,7 +154,8 @@ impl TransportClient {
         let method = request.method().clone();
         let url = request.url().to_string();
 
-        match self.execute_without_request_logging(request).await {
+        let result = self.execute_without_request_logging(request).await;
+        match result {
             Ok(response) => {
                 self.log_response(&method, &url, &response);
                 Ok(response)

codex-rs/http-client/src/local_staging_routing.rs

@@ -0,0 +1 @@
+

codex-rs/http-client/src/local_staging_routing_tests.rs

@@ -0,0 +1 @@
+

codex-rs/http-client/src/route_aware_client_pool/execution.rs

@@ -322,7 +322,8 @@ impl RouteAwareClientPool {
         let client = self.windows_proxy_client(current_route, selected_tls_backend, &pipe)?;
         set_remaining_timeout(&mut request, timeout_deadline)?;
         // Keep the listener alive through a possible TLS retry.
-        match client.execute_without_request_logging(request).await {
+        let result = client.execute_without_request_logging(request).await;
+        match result {
             Ok(response) => Ok(response),
             Err(error) => {
                 self.retry_with_rustls(