feat: add header for task kind (#5142)

Add a header in the responses API request for the task kind (compact,
review, ...) for observability purpose
The header name is `codex-task-type`

codex-rs/core/tests/responses_headers.rs

@@ -0,0 +1,102 @@
+use std::sync::Arc;
+
+use codex_app_server_protocol::AuthMode;
+use codex_core::ContentItem;
+use codex_core::ModelClient;
+use codex_core::ModelProviderInfo;
+use codex_core::Prompt;
+use codex_core::ResponseEvent;
+use codex_core::ResponseItem;
+use codex_core::WireApi;
+use codex_otel::otel_event_manager::OtelEventManager;
+use codex_protocol::ConversationId;
+use core_test_support::load_default_config_for_test;
+use core_test_support::responses;
+use futures::StreamExt;
+use tempfile::TempDir;
+use wiremock::matchers::header;
+
+#[tokio::test]
+async fn responses_stream_includes_task_type_header() {
+    core_test_support::skip_if_no_network!();
+
+    let server = responses::start_mock_server().await;
+    let response_body = responses::sse(vec![
+        responses::ev_response_created("resp-1"),
+        responses::ev_completed("resp-1"),
+    ]);
+
+    let request_recorder = responses::mount_sse_once_match(
+        &server,
+        header("Codex-Task-Type", "standard"),
+        response_body,
+    )
+    .await;
+
+    let provider = ModelProviderInfo {
+        name: "mock".into(),
+        base_url: Some(format!("{}/v1", server.uri())),
+        env_key: None,
+        env_key_instructions: None,
+        wire_api: WireApi::Responses,
+        query_params: None,
+        http_headers: None,
+        env_http_headers: None,
+        request_max_retries: Some(0),
+        stream_max_retries: Some(0),
+        stream_idle_timeout_ms: Some(5_000),
+        requires_openai_auth: false,
+    };
+
+    let codex_home = TempDir::new().expect("failed to create TempDir");
+    let mut config = load_default_config_for_test(&codex_home);
+    config.model_provider_id = provider.name.clone();
+    config.model_provider = provider.clone();
+    let effort = config.model_reasoning_effort;
+    let summary = config.model_reasoning_summary;
+    let config = Arc::new(config);
+
+    let conversation_id = ConversationId::new();
+
+    let otel_event_manager = OtelEventManager::new(
+        conversation_id,
+        config.model.as_str(),
+        config.model_family.slug.as_str(),
+        None,
+        Some(AuthMode::ChatGPT),
+        false,
+        "test".to_string(),
+    );
+
+    let client = ModelClient::new(
+        Arc::clone(&config),
+        None,
+        otel_event_manager,
+        provider,
+        effort,
+        summary,
+        conversation_id,
+    );
+
+    let mut prompt = Prompt::default();
+    prompt.input = vec![ResponseItem::Message {
+        id: None,
+        role: "user".into(),
+        content: vec![ContentItem::InputText {
+            text: "hello".into(),
+        }],
+    }];
+
+    let mut stream = client.stream(&prompt).await.expect("stream failed");
+    while let Some(event) = stream.next().await {
+        if matches!(event, Ok(ResponseEvent::Completed { .. })) {
+            break;
+        }
+    }
+
+    let request = request_recorder.single_request();
+    assert_eq!(
+        request.header("Codex-Task-Type").as_deref(),
+        Some("standard")
+    );
+}