Expose cached MCP tools before server startup (#35590)

## Why

Cached MCP definitions can be supplied to inference without waiting for the
server to finish initializing.

## What changed

- Publish cached tools while startup is still in progress, clearing their
  potentially stale read-only hint.
- Wait for the selected server to start before executing a tool call, then
  prepare the call against the refreshed live binding.
- Keep cached tools visible in a binding even when no live client is available,
  while rejecting attempts to prepare those calls.

## Testing

- Cover cached-tool visibility before startup and replacement with live tool
  metadata afterward.
- Verify cached definitions reach inference before MCP initialization and that
  calls unavailable in the live catalog return the expected model-visible
  error.

GitOrigin-RevId: 3aae8f474c344ccdc5e08fe321bbad21d85bffd1

codex-rs/codex-mcp/src/runtime.rs

@@ -240,6 +240,21 @@ impl McpRuntime {
         }
     }
 
+    /// Captures the current runtime after its selected server has finished startup.
+    pub async fn current_binding_for_call(&self, server: &str) -> Option<Arc<McpBinding>> {
+        let current = self.current.load_full();
+        let config = Arc::clone(current.config.as_ref()?);
+        if !current.connections.wait_for_server_startup(server).await {
+            return None;
+        }
+        Some(Arc::new(
+            current
+                .connections
+                .capture_binding_with_metadata(config, current.plugins_available)
+                .await,
+        ))
+    }
+
     /// Returns the latest published configuration without waiting for clients.
     pub fn current_config(&self) -> Option<Arc<McpConfig>> {
         self.current.load().config.clone()