[MCP] Add auth status to MCP servers (#4918)

This adds a queryable auth status for MCP servers which is useful:
1. To determine whether a streamable HTTP server supports auth or not
based on whether or not it supports RFC 8414-3.2
2. Allow us to build a better user experience on top of MCP status

codex-rs/core/src/codex.rs

@@ -57,6 +57,7 @@ use crate::exec_command::WriteStdinParams;
 use crate::executor::Executor;
 use crate::executor::ExecutorConfig;
 use crate::executor::normalize_exec_result;
+use crate::mcp::auth::compute_auth_statuses;
 use crate::mcp_connection_manager::McpConnectionManager;
 use crate::model_family::find_family_for_model;
 use crate::openai_model_info::get_model_info;
@@ -1403,10 +1404,18 @@ async fn submission_loop(
 
                 // This is a cheap lookup from the connection manager's cache.
                 let tools = sess.services.mcp_connection_manager.list_all_tools();
+                let auth_statuses = compute_auth_statuses(
+                    config.mcp_servers.iter(),
+                    config.mcp_oauth_credentials_store_mode,
+                )
+                .await;
                 let event = Event {
                     id: sub_id,
                     msg: EventMsg::McpListToolsResponse(
-                        crate::protocol::McpListToolsResponseEvent { tools },
+                        crate::protocol::McpListToolsResponseEvent {
+                            tools,
+                            auth_statuses,
+                        },
                     ),
                 };
                 sess.send_event(event).await;