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/src/endpoint/chat.rs

@@ -87,6 +87,7 @@ impl<T: HttpTransport, A: AuthProvider> ChatClient<T, A> {
                 extra_headers,
                 RequestCompression::None,
                 spawn_chat_stream,
+                None,
             )
             .await
     }