如何在Flutter上使用ChangeNotifierProvider选择另一个选项卡时更改AppBar颜色？

dependencies:
  flutter:
    sdk: flutter
  provider: ^5.0.0

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

class TabIndexModel extends ChangeNotifier {
  int _selectedIndex = 0;

  int get selectedIndex => _selectedIndex;

  void setTabIndex(int index) {
    _selectedIndex = index;
    notifyListeners();
  }
}

void main() {
  runApp(
    ChangeNotifierProvider(
      create: (context) => TabIndexModel(),
      child: MyApp(),
    ),
  );
}

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter ChangeNotifierProvider Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: MyHomePage(),
    );
  }
}

class MyHomePage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        backgroundColor: _getAppBarColor(context),
        title: Text('Flutter ChangeNotifierProvider Demo'),
      ),
      body: Consumer<TabIndexModel>(
        builder: (context, tabIndexModel, child) {
          return Column(
            children: [
              TabBar(
                tabs: [
                  Tab(text: 'Tab 1'),
                  Tab(text: 'Tab 2'),
                  Tab(text: 'Tab 3'),
                ],
                onTap: (index) {
                  tabIndexModel.setTabIndex(index);
                },
              ),
              Expanded(
                child: _buildTabContent(tabIndexModel.selectedIndex),
              ),
            ],
          );
        },
      ),
    );
  }

  Color _getAppBarColor(BuildContext context) {
    final tabIndexModel = Provider.of<TabIndexModel>(context);
    switch (tabIndexModel.selectedIndex) {
      case 0:
        return Colors.blue;
      case 1:
        return Colors.green;
      case 2:
        return Colors.red;
      default:
        return Colors.blue;
    }
  }

  Widget _buildTabContent(int index) {
    switch (index) {
      case 0:
        return Container(
          color: Colors.blue,
          child: Center(child: Text('Tab 1')),
        );
      case 1:
        return Container(
          color: Colors.green,
          child: Center(child: Text('Tab 2')),
        );
      case 2:
        return Container(
          color: Colors.red,
          child: Center(child: Text('Tab 3')),
        );
      default:
        return Container();
    }
  }
}