Reuse stable MCP bindings across sampling steps (#37101)

## What changed

- Cache an `McpBinding` on each published MCP runtime once server startup has
  settled and the tool catalog revision is stable.
- Reuse the cached binding while the catalog revision remains unchanged, and
  rebuild it after a runtime publish or catalog change.
- Treat terminal failures from optional servers as stable, while continuing to
  wait for required servers and reconnecting Codex Apps servers.

## Testing

- Cover binding reuse within one published runtime and invalidation after a
  republish.
- Cover stability checks for pending, failed optional, required, and
  reconnected servers.

GitOrigin-RevId: 783a6b04897f6c484a6d56fd9cee542814041759

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

@@ -492,6 +492,24 @@ impl AsyncManagedClient {
         self.client.clone().await
     }
 
+    pub(crate) fn ready_transport(&self) -> Option<Arc<RmcpClient>> {
+        let recovered = self.startup_reconnect.as_ref().and_then(|reconnect| {
+            reconnect
+                .state
+                .lock()
+                .unwrap_or_else(std::sync::PoisonError::into_inner)
+                .current_client
+                .as_ref()
+                .map(|client| Arc::clone(&client.client))
+        });
+        recovered.or_else(|| {
+            self.client
+                .peek()
+                .and_then(|result| result.as_ref().ok())
+                .map(|client| Arc::clone(&client.client))
+        })
+    }
+
     pub(crate) async fn reconnect_failed_startup(&self) {
         let Some(startup_reconnect) = self.startup_reconnect.as_ref() else {
             return;