How does the InheritedWidget class let data genuinely and efficiently propagate down through the widget tree to any descendant widget that specifically needs it, without requiring that same data to be manually passed down explicitly through every single individual intermediate widget constructor along the way?

InheritedWidget is a genuinely special kind of widget specifically designed to efficiently make a given piece of data available to any descendant widget anywhere further down within the overall widget tree, without requiring that same particular data to be manually and explicitly passed down individually through every single intermediate widget constructor along the entire way, and any descendant widget can then properly access that specific shared data simply by calling a corresponding static method, such as Theme.of or MediaQuery.of, both of which are themselves genuinely and actually implemented internally using exactly this same underlying InheritedWidget mechanism, and Flutter's own popular state management packages, including Provider, are themselves also genuinely built directly on top of this exact same underlying core mechanism.

class MyInheritedData extends InheritedWidget {
  final String data;
  const MyInheritedData({required this.data, required super.child});

  static MyInheritedData of(BuildContext context) =>
    context.dependOnInheritedWidgetOfType<MyInheritedData>()!;

  @override
  bool updateShouldNotify(MyInheritedData oldWidget) => data != oldWidget.data;
}