Turn-state sticky routing per turn (#9332)

- capture the header from SSE/WS handshakes, store it per
ModelClientSession using `Oncelock`, echo it on turn-scoped requests,
and add SSE+WS integration tests for within-turn persistence +
cross-turn reset.

- keep `x-codex-turn-state` sticky within a user turn to maintain
routing continuity for retries/tool follow-ups.

codex-rs/codex-api/tests/clients.rs

@@ -231,7 +231,7 @@ async fn responses_client_uses_responses_path_for_responses_wire() -> Result<()>
 
     let body = serde_json::json!({ "echo": true });
     let _stream = client
-        .stream(body, HeaderMap::new(), Compression::None)
+        .stream(body, HeaderMap::new(), Compression::None, None)
         .await?;
 
     let requests = state.take_stream_requests();
@@ -247,7 +247,7 @@ async fn responses_client_uses_chat_path_for_chat_wire() -> Result<()> {
 
     let body = serde_json::json!({ "echo": true });
     let _stream = client
-        .stream(body, HeaderMap::new(), Compression::None)
+        .stream(body, HeaderMap::new(), Compression::None, None)
         .await?;
 
     let requests = state.take_stream_requests();
@@ -264,7 +264,7 @@ async fn streaming_client_adds_auth_headers() -> Result<()> {
 
     let body = serde_json::json!({ "model": "gpt-test" });
     let _stream = client
-        .stream(body, HeaderMap::new(), Compression::None)
+        .stream(body, HeaderMap::new(), Compression::None, None)
         .await?;
 
     let requests = state.take_stream_requests();

codex-rs/codex-api/tests/sse_end_to_end.rs

@@ -129,6 +129,7 @@ async fn responses_stream_parses_items_and_completed_end_to_end() -> Result<()>
             serde_json::json!({"echo": true}),
             HeaderMap::new(),
             Compression::None,
+            None,
         )
         .await?;
 
@@ -198,6 +199,7 @@ async fn responses_stream_aggregates_output_text_deltas() -> Result<()> {
             serde_json::json!({"echo": true}),
             HeaderMap::new(),
             Compression::None,
+            None,
         )
         .await?;