Responses: set x-client-request-id as convesration_id when talking to responses (#14312)

Right now we're sending the header session_id to responses which is
ignored/dropped. This sets a useful x-client-request-id to the
conversation_id.

codex-rs/codex-api/src/endpoint/responses.rs

@@ -75,6 +75,9 @@ impl<T: HttpTransport, A: AuthProvider> ResponsesClient<T, A> {
         }
 
         let mut headers = extra_headers;
+        if let Some(ref conv_id) = conversation_id {
+            insert_header(&mut headers, "x-client-request-id", conv_id);
+        }
         headers.extend(build_conversation_headers(conversation_id));
         if let Some(subagent) = subagent_header(&session_source) {
             insert_header(&mut headers, "x-openai-subagent", &subagent);

codex-rs/core/src/client.rs

@@ -487,14 +487,16 @@ impl ModelClient {
         turn_metadata_header: Option<&str>,
     ) -> ApiHeaderMap {
         let turn_metadata_header = parse_turn_metadata_header(turn_metadata_header);
+        let conversation_id = self.state.conversation_id.to_string();
         let mut headers = build_responses_headers(
             self.state.beta_features_header.as_deref(),
             turn_state,
             turn_metadata_header.as_ref(),
         );
-        headers.extend(build_conversation_headers(Some(
-            self.state.conversation_id.to_string(),
-        )));
+        if let Ok(header_value) = HeaderValue::from_str(&conversation_id) {
+            headers.insert("x-client-request-id", header_value);
+        }
+        headers.extend(build_conversation_headers(Some(conversation_id)));
         headers.insert(
             OPENAI_BETA_HEADER,
             HeaderValue::from_static(RESPONSES_WEBSOCKETS_V2_BETA_HEADER_VALUE),

codex-rs/core/tests/suite/client_websockets.rs

@@ -49,10 +49,12 @@ use tracing_test::traced_test;
 const MODEL: &str = "gpt-5.2-codex";
 const OPENAI_BETA_HEADER: &str = "OpenAI-Beta";
 const WS_V2_BETA_HEADER_VALUE: &str = "responses_websockets=2026-02-06";
+const X_CLIENT_REQUEST_ID_HEADER: &str = "x-client-request-id";
 
 struct WebsocketTestHarness {
     _codex_home: TempDir,
     client: ModelClient,
+    conversation_id: ThreadId,
     model_info: ModelInfo,
     effort: Option<ReasoningEffortConfig>,
     summary: ReasoningSummary,
@@ -88,6 +90,10 @@ async fn responses_websocket_streams_request() {
         handshake.header(OPENAI_BETA_HEADER),
         Some(WS_V2_BETA_HEADER_VALUE.to_string())
     );
+    assert_eq!(
+        handshake.header(X_CLIENT_REQUEST_ID_HEADER),
+        Some(harness.conversation_id.to_string())
+    );
 
     server.shutdown().await;
 }
@@ -1606,6 +1612,7 @@ async fn websocket_harness_with_options(
     WebsocketTestHarness {
         _codex_home: codex_home,
         client,
+        conversation_id,
         model_info,
         effort,
         summary,