flutter not showing files, only folders

Question

I am trying to build a flutter app for Android, to show all the directories and files inside a device directory, for example the '/storage/emulated/0'. The app is able to show all the directories, but unfortunately the files do not show up. I copy below the code of the main.dart file:

import 'dart:io';
import 'package:flutter/material.dart';

void main() {
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'File Browser',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: const MyHomePage(),
    );
  }
}

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

  @override
  _MyHomePageState createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  List<FileSystemEntity> _files = [];

  @override
  void initState() {
    super.initState();
    _getFiles();
  }

  Future<void> _getFiles() async {
    try {
      Directory directory = Directory(
          '/storage/emulated/0');
      List<FileSystemEntity> files = directory.listSync();
      setState(() {
        _files = files;
      });
    } catch (e) {
      print('Error reading directory: $e');
    }
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: const Text('File Browser'),
      ),
      body: ListView.builder(
        itemCount: _files.length,
        itemBuilder: (context, index) {
          FileSystemEntity file = _files[index];
          return ListTile(
            title: Text(file.toString()),
          );
        },
      ),
    );
  }
}

Searching on the internet I discovered that, since Android 11, some permissions are necessary to access the files. So I added all the following permissions in the AndroidManifest.xml, but the files still do not show up.

<manifest xmlns:android="http://schemas.android.com/apk/res/android">
    <uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE"/>
    <uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE"/>
    <uses-permission android:name="android.permission.ACTION_MANAGE_ALL_FILES_ACCESS_PERMISSION"/>
    <uses-permission android:name="android.permission.MANAGE_EXTERNAL_STORAGE"/>

For completion, I add below also the code of the pubspec.yaml file

name: file_browser
description: "A new Flutter project."
publish_to: 'none' # Remove this line if you wish to publish to pub.dev
version: 1.0.0+1
environment:
  sdk: '>=3.3.1 <4.0.0'
dependencies:
  flutter:
    sdk: flutter
  cupertino_icons: ^1.0.6
dev_dependencies:
  flutter_test:
    sdk: flutter
  flutter_lints: ^3.0.0
flutter:
  uses-material-design: true

Thank you so much to anyone will try to help.