Improve MCP server startup error logging (#42370)

## What changed

- Log failed MCP server startup outcomes once per startup attempt, including failures during discovery that do not emit startup notifications.
- Preserve the full error chain when converting startup failures into cloneable outcome errors.

GitOrigin-RevId: 54bbf2abaf3329d9828b2d2bc5d877fddc2917e1

codex-rs/codex-mcp/src/rmcp_client.rs

@@ -362,7 +362,7 @@ impl ManagedClientStartup {
                     }
                 };
                 start_server_task(
-                    server_name,
+                    server_name.clone(),
                     client,
                     StartServerTaskParams {
                         is_codex_apps_mcp_server,
@@ -385,6 +385,10 @@ impl ManagedClientStartup {
                 Ok(result) => result,
                 Err(CancelErr::Cancelled) => Err(StartupOutcomeError::Cancelled),
             };
+            // Log once per startup attempt, including discovery without startup notifications.
+            if let Err(StartupOutcomeError::Failed { error, .. }) = &outcome {
+                warn!(server_name, %error, "MCP server startup failed");
+            }
             if outcome.is_ok()
                 && let Some(refresh_start) = refresh_start
             {
@@ -618,7 +622,7 @@ impl From<anyhow::Error> for StartupOutcomeError {
     fn from(error: anyhow::Error) -> Self {
         let is_authentication_required = is_authentication_required_error(&error);
         Self::Failed {
-            error: error.to_string(),
+            error: format!("{error:#}"),
             is_authentication_required,
         }
     }