[codex] Wait for MCP readiness in core integration tests (#24964)

Ensures MCP-backed `codex-core` integration tests exercise initialized
servers instead of racing server startup.

I've been idly investigating a few flakes and the failure modes are much
more confusing when a tool call fails because of a failed server start
than when the failed server start causes the test to fail directly.

codex-rs/core/tests/common/lib.rs

@@ -248,6 +248,39 @@ where
     wait_for_event_with_timeout(codex, predicate, Duration::from_secs(1)).await
 }
 
+/// Waits for a configured MCP server to finish startup and requires it to be ready.
+pub async fn wait_for_mcp_server(codex: &CodexThread, server_name: &str) -> anyhow::Result<()> {
+    use codex_protocol::protocol::EventMsg;
+
+    // Wait for the startup summary regardless of outcome, then interpret the
+    // requested server's ready, failed, or cancelled entry below.
+    let summary = loop {
+        let event = codex
+            .next_event()
+            .await
+            .expect("stream ended unexpectedly while waiting for MCP startup");
+        if let EventMsg::McpStartupComplete(summary) = event.msg {
+            break summary;
+        }
+    };
+    if let Some(failure) = summary
+        .failed
+        .iter()
+        .find(|failure| failure.server == server_name)
+    {
+        let error = &failure.error;
+        anyhow::bail!("MCP server {server_name} failed to start: {error}");
+    }
+    if summary.cancelled.iter().any(|server| server == server_name) {
+        anyhow::bail!("MCP server {server_name} startup was cancelled");
+    }
+    assert!(
+        summary.ready.iter().any(|server| server == server_name),
+        "expected MCP server {server_name} to be ready; startup summary: {summary:?}"
+    );
+    Ok(())
+}
+
 pub async fn submit_thread_settings(
     codex: &CodexThread,
     thread_settings: codex_protocol::protocol::ThreadSettingsOverrides,