[flutter_tools] modify Skeleton template to use ListenableBuilder instead of AnimatedBuilder (#128810)

Replaces AnimatedBuilder for ListenableBuilder in the skeleton template

Fixes https://github.com/flutter/flutter/issues/128801

No tests needed

packages/flutter_tools/templates/skeleton/lib/src/app.dart.tmpl

@@ -20,10 +20,10 @@ class MyApp extends StatelessWidget {
   Widget build(BuildContext context) {
     // Glue the SettingsController to the MaterialApp.
     //
-    // The AnimatedBuilder Widget listens to the SettingsController for changes.
+    // The ListenableBuilder Widget listens to the SettingsController for changes.
     // Whenever the user updates their settings, the MaterialApp is rebuilt.
-    return AnimatedBuilder(
-      animation: settingsController,
+    return ListenableBuilder(
+      listenable: settingsController,
       builder: (BuildContext context, Widget? child) {
         return MaterialApp(
           // Providing a restorationScopeId allows the Navigator built by the