Flutter - Accessing a Provider from a higher point in the Widget tree - flutter

Question

I've been working with Flutter recently, and I saw that there was many ways to deal with state management.
Following the recommendations there, I've been using Provider to deal with the state of my app.
I can update a part of my state from one of the widgets in my UI. To do that, I can call a method of the provider that's above the current widget in the context. No problems with this.
But I want the update of my state to be made from an overlay.
The issue is: When I'm inserting an OverlayEntry with Overlay.of(context)?.insert(), it inserts the overlayEntry to the closest Overlay, which is in general the root of the app, which is above the ChangeProvider. As a result, I get an exception saying I can't find the Provider from the OverlayEntry.
Here is a replication code I've been writting:
import 'package:flutter/material.dart';
import 'package:provider/provider.dart';
void main() {
runApp(const MyApp());
}
class MyApp extends StatelessWidget {
const MyApp({super.key});
#override
Widget build(BuildContext context) {
return MaterialApp(
theme: ThemeData(
primarySwatch: Colors.blue,
),
home: ChangeNotifierProvider(
create: (context) => NumberModel(), // All widgets that will be lower in the widget tree will have access to NumberModel
child: NumberDisplayer()
),
);
}
}
// Simple ChangeNotifier. We have a number that we can increment.
class NumberModel extends ChangeNotifier {
int _number = 10;
int get number => _number;
void add_one() {
_number = number + 1;
notifyListeners();
}
}
// This class displays a number, and a button.
class NumberDisplayer extends StatelessWidget {
NumberDisplayer({Key? key}) : super(key: key);
#override
Widget build(BuildContext context) {
var overlayEntry = OverlayEntry(builder: (context) =>
Positioned(
top: 100,
left: 50,
child: FloatingActionButton(onPressed: (){
// Throws "Error: Could not find the correct Provider<NumberModel> above this _OverlayEntryWidget Widget"
Provider.of<NumberModel>(context, listen: false).add_one();
})));
return Consumer<NumberModel>(
builder: (context, numberModel, child) {
return Column(
children: [
Text('Number: ${numberModel.number}'),
FloatingActionButton(onPressed: () {
Overlay.of(context)?.insert(overlayEntry);
})
],
);
},
);
}
}
I would like to find a way to update the information in my provider from the overlay, but I'm not sure how to approach this problem.
Thanks for your help everyone !