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/core/src/mcp_tool_call.rs

@@ -141,7 +141,11 @@ pub(crate) async fn handle_mcp_tool_call(
     };
 
     sess.refresh_mcp_if_dirty().await;
-    let current_binding = sess.services.mcp_runtime.current_binding().await;
+    let current_binding = sess
+        .services
+        .mcp_runtime
+        .current_binding_for_call(&server)
+        .await;
     let Some(prepared_call) = current_binding
         .as_ref()
         .and_then(|binding| binding.prepare_call(&server, &tool_name))