Fix Codex Apps auth elicitation hang (#29615)

## Summary
- Require the reserved Codex Apps MCP server name to be present in the
connection manager before treating it as host-owned.
- Update auth elicitation tests to model an installed host-owned Codex
Apps server without sending startup events to the test session.

## Why
PR #29518 replaced the old host-owned flag with a name-only check. That
made non-host-owned tests with the reserved codex_apps name enter auth
elicitation and wait forever for a response.

codex-rs/codex-mcp/src/connection_manager.rs

@@ -391,7 +391,7 @@ impl McpConnectionManager {
     }
 
     pub fn is_host_owned_codex_apps_server(&self, server_name: &str) -> bool {
-        server_name == CODEX_APPS_MCP_SERVER_NAME
+        server_name == CODEX_APPS_MCP_SERVER_NAME && self.server_metadata.contains_key(server_name)
     }
 
     pub fn set_approval_policy(&self, approval_policy: &Constrained<AskForApproval>) {

codex-rs/codex-mcp/src/connection_manager_tests.rs

@@ -1177,6 +1177,41 @@ fn server_metadata_preserves_tool_approval_policy() {
     );
 }
 
+#[test]
+fn host_owned_codex_apps_requires_server_metadata() {
+    let approval_policy = Constrained::allow_any(AskForApproval::OnFailure);
+    let permission_profile = Constrained::allow_any(PermissionProfile::default());
+    let manager = McpConnectionManager::new_uninitialized(
+        &approval_policy,
+        &permission_profile,
+        /*prefix_mcp_tool_names*/ true,
+    );
+
+    assert!(!manager.is_host_owned_codex_apps_server(CODEX_APPS_MCP_SERVER_NAME));
+}
+
+#[test]
+fn host_owned_codex_apps_matches_reserved_name_with_server_metadata() {
+    let approval_policy = Constrained::allow_any(AskForApproval::OnFailure);
+    let permission_profile = Constrained::allow_any(PermissionProfile::default());
+    let mut manager = McpConnectionManager::new_uninitialized(
+        &approval_policy,
+        &permission_profile,
+        /*prefix_mcp_tool_names*/ true,
+    );
+    let server = EffectiveMcpServer::configured(crate::codex_apps_mcp_server_config(
+        "https://chatgpt.com",
+        /*apps_mcp_product_sku*/ None,
+    ));
+    manager.server_metadata.insert(
+        CODEX_APPS_MCP_SERVER_NAME.to_string(),
+        McpServerMetadata::from(&server),
+    );
+
+    assert!(manager.is_host_owned_codex_apps_server(CODEX_APPS_MCP_SERVER_NAME));
+    assert!(!manager.is_host_owned_codex_apps_server("docs"));
+}
+
 #[tokio::test]
 async fn no_local_runtime_fails_local_stdio_but_keeps_local_http_server() {
     let approval_policy = Constrained::allow_any(AskForApproval::OnFailure);

codex-rs/core/src/mcp_tool_call_tests.rs

@@ -1335,15 +1335,25 @@ fn codex_apps_auth_failure_metadata() -> McpToolApprovalMetadata {
 
 async fn install_host_owned_codex_apps_manager(session: &Session, turn_context: &TurnContext) {
     let auth = session.services.auth_manager.auth().await;
+    let startup_cancellation_token = CancellationToken::new();
+    startup_cancellation_token.cancel();
+    let (tx_event, _rx_event) = async_channel::unbounded();
+    let mcp_servers = HashMap::from([(
+        CODEX_APPS_MCP_SERVER_NAME.to_string(),
+        codex_mcp::EffectiveMcpServer::configured(codex_mcp::codex_apps_mcp_server_config(
+            "https://chatgpt.com",
+            /*apps_mcp_product_sku*/ None,
+        )),
+    )]);
     let manager = codex_mcp::McpConnectionManager::new(
-        &HashMap::new(),
+        &mcp_servers,
         turn_context.config.mcp_oauth_credentials_store_mode,
         turn_context.config.auth_keyring_backend_kind(),
         HashMap::new(),
         &turn_context.approval_policy,
         turn_context.sub_id.clone(),
-        session.get_tx_event(),
-        CancellationToken::new(),
+        tx_event,
+        startup_cancellation_token,
         turn_context.permission_profile(),
         codex_mcp::McpRuntimeContext::new(
             session.services.turn_environments.environment_manager(),