Allow cached catalogs to satisfy MCP startup readiness (#47935)

## Why

Required MCP servers can block startup while establishing a live connection even when a usable tool catalog is already cached.

## What changed

- Add per-server `startup_readiness = "catalog"` to expose cached tools while the connection starts, retaining `"connection"` as the default.
- Allow an eligible cached catalog to satisfy required-server startup validation and model binding capture. Explicit server or plugin requirements still wait for a live connection, and tool execution still requires the current connection.
- Check tool filters and model visibility when accepting cached catalogs, and preserve cached catalog revisions for binding reuse.
- Serialize the new setting, expose it in the configuration schema, and trace startup readiness at validation and model binding gates.

GitOrigin-RevId: a1cbdf1757ebb5824cffe2cc56408be49711c422

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

@@ -417,12 +417,13 @@ impl McpRuntime {
         required_servers: &[String],
         required_plugins: &HashSet<String>,
     ) -> Option<Arc<McpBinding>> {
-        Self::binding_from_published_runtime(
-            self.current.load_full(),
+        let current = self.current.load_full();
+        current.connections.record_startup_readiness(
+            "model_binding",
             required_servers,
             required_plugins,
-        )
-        .await
+        );
+        Self::binding_from_published_runtime(current, required_servers, required_plugins).await
     }
 
     async fn binding_from_published_runtime(
@@ -948,6 +949,7 @@ mod tests {
             environment_id: environment_id.to_string(),
             enabled: true,
             required: false,
+            startup_readiness: Default::default(),
             supports_parallel_tool_calls: false,
             omit_tools_from: None,
             disabled_reason: None,