Separate HTTP execution from request logging (#34476)

## What changed

- Add an execution path that injects trace headers and sends a request without
  logging its result.
- Extract response and error logging into reusable helpers while preserving the
  existing behavior of `HttpClient::execute`.

GitOrigin-RevId: 3feebe3da041dd08f5033dd319233d8afe9054ec

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

@@ -69,14 +69,32 @@ impl HttpClient {
 
     pub(crate) async fn execute(
         &self,
-        mut request: reqwest::Request,
+        request: reqwest::Request,
     ) -> Result<reqwest::Response, reqwest::Error> {
-        request.headers_mut().extend(trace_headers());
         let method = request.method().clone();
         let url = request.url().to_string();
 
-        match self.inner.execute(request).await {
+        match self.execute_without_request_logging(request).await {
             Ok(response) => {
+                self.log_response(&method, &url, &response);
+                Ok(response)
+            }
+            Err(error) => {
+                self.log_error(&method, &url, &error);
+                Err(error)
+            }
+        }
+    }
+
+    pub(crate) async fn execute_without_request_logging(
+        &self,
+        mut request: reqwest::Request,
+    ) -> Result<reqwest::Response, reqwest::Error> {
+        request.headers_mut().extend(trace_headers());
+        self.inner.execute(request).await
+    }
+
+    pub(crate) fn log_response(&self, method: &Method, url: &str, response: &reqwest::Response) {
         if self.request_logging == RequestLogging::Enabled {
             tracing::debug!(
                 method = %method,
@@ -87,9 +105,9 @@ impl HttpClient {
                 "Request completed"
             );
         }
-                Ok(response)
     }
-            Err(error) => {
+
+    pub(crate) fn log_error(&self, method: &Method, url: &str, error: &reqwest::Error) {
         if self.request_logging == RequestLogging::Enabled {
             tracing::debug!(
                 method = %method,
@@ -99,9 +117,6 @@ impl HttpClient {
                 "Request failed"
             );
         }
-                Err(error)
-            }
-        }
     }
 }