Call a function in deep child in widget tree if some event occurs in top level widget in flutter

You can use InheritedWidget

class MyInheritedData extends InheritedWidget {
  const MyInheritedData({
    super.key,
    required super.child,
    required this.valueChangedBySomeEvent,
    this.someFunction,
  });

  final dynamic valueChangedBySomeEvent;
  final Function()? someFunction;

  static MyInheritedData of(BuildContext context) {
    final MyInheritedData? result = context.dependOnInheritedWidgetOfExactType<MyInheritedData>();
    assert(result != null, 'No MyInheritedWidget found in context');
    return result!;
  }

  @override
  bool updateShouldNotify(MyInheritedData oldWidget) {
    // your condition can be customized here
    return valueChangedBySomeEvent != oldWidget.valueChangedBySomeEvent &&
    someFunction != oldWidget.someFunction;
  }
}

class Widget1 extends StatefulWidget {
  const Widget1({super.key, required this.child});
  
  final Widget child;

  @override
  State<Widget1> createState() => _Widget1State();
}

class _Widget1State extends State<Widget1> {
  bool valueChangedBySomeEvent = false;
  
  someEvent() {
    setState(() {
      valueChangedBySomeEvent = !valueChangedBySomeEvent;
    });
  }
  
  @override
  Widget build(BuildContext context) {
    return GestureDetector(
      onTap: someEvent,
      child: MyInheritedData(
        valueChangedBySomeEvent: valueChangedBySomeEvent,
        child: widget.child,
      ),
    );
  }
}

class Widget4 extends StatefulWidget {
  const Widget4({super.key});

  @override
  State<Widget4> createState() => _Widget4State();
}

class _Widget4State extends State<Widget4> {
  
  @override
  void didChangeDependencies() {
    final myInheritedData = MyInheritedData.of(context);
    // callFunction (you can add some conditions here also)
    myInheritedData.someFunction?.call();
    super.didChangeDependencies();
  }

  @override
  Widget build(BuildContext context) {
    return Container();
  }
}

whenever the parent widget of MyInheritedData is built, (Widget1) MyInheritedData.updateShouldNotify is triggered and if it returns true,
then all descendants (Widget4) will trigger their didChangeDependencies.

Edit

InheritedWidget is built in flutter. you can use a state management package if you want to write less code. here is an example using riverpod:

void main() {
  // wrap your entire application with ProviderScope to
  // enable riverpod
  runApp(const ProviderScope(child: MyApp()));
}

// you can access this provider anywhere in your app
final triggerProvider = StateProvider<bool>((ref) => true);

class Widget1 extends ConsumerWidget {
  const Widget1({super.key});

  someEvent(WidgetRef ref) {
    if (true) {
      // toggle triggerProvider whenever the condition is true
      ref.read(triggerProvider.notifier).update((state) => !state);
    }
  }

  @override
  Widget build(BuildContext context, WidgetRef ref) {

    return GestureDetector(
      onTap: () => someEvent(ref),
    );
  }
}

class Widget4 extends ConsumerWidget {
  const Widget4({super.key});

  someFunction() {}

  @override
  Widget build(BuildContext context, WidgetRef ref) {

    ref.listen(triggerProvider, (previous, next) {
      // call your function whenever the provider is toggled
      someFunction();
    });

    return Container();
  }
}