How to navigator.pushReplacement from BottomNavigationBar in Flutter

I'm building an app which contains bottomnaviationbaritem, Currently there are two tab items (Home Page and Search Page) and in search page there is a button. So what i want to do is if i click on the button in Search Page i want to call open homepage and homepage bar item should be selected just like an open the app from scratch or from starting. So how to achieve this because i tried this code navigator.pushreplacement which displays two bottom navigation bar at the bottom. I hope you understand my question.

main.dart

Future<void> main() async {
  WidgetsFlutterBinding.ensureInitialized();
  runApp(MyApp());
}
class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      debugShowCheckedModeBanner: false,
      home: App(),
    );
  }
}
class App extends StatefulWidget {
  @override
  State<StatefulWidget> createState() => AppState();
}
class AppState extends State<App> {
  static int currentTab = 0;
  final List<TabItem> tabs = [
    TabItem(
      tabName: "Home",
      icon: Icons.home_outlined,
      page: HomePage(),
    ),
    TabItem(
      tabName: "Search",
      icon: Icons.search,
      page: SearchPage(),
    ),
  ];
  AppState() {
    tabs.asMap().forEach((index, details) {
      details.setIndex(index);
    });
  }
  void _selectTab(int index) {
    if (index == currentTab) {
      tabs[index].key.currentState!.popUntil((route) => route.isFirst);
    } else {
      setState(() => currentTab = index);
    }
  }
  @override
  Widget build(BuildContext context) {
    return WillPopScope(
      onWillPop: () async {
        final isFirstRouteInCurrentTab =
        !await tabs[currentTab].key.currentState!.maybePop();
        if (isFirstRouteInCurrentTab) {
          if (currentTab != 0) {
            _selectTab(0);
            return false;
          }
        }
        return isFirstRouteInCurrentTab;
      },
      child: Scaffold(
        body: IndexedStack(
          index: currentTab,
          children: tabs.map((e) => e.page).toList(),
        ),
        bottomNavigationBar: BottomNavigation(
          onSelectTab: _selectTab,
          tabs: tabs,
        ),
      ),
    );
  }
}

BottomNavigation.dart

class BottomNavigation extends StatelessWidget {
  BottomNavigation({
    required this.onSelectTab,
    required this.tabs,
  });
  final ValueChanged<int> onSelectTab;
  final List<TabItem> tabs;
  @override
  Widget build(BuildContext context) {
    return BottomNavigationBar(
      type: BottomNavigationBarType.fixed,
      items: tabs
          .map(
            (e) => _buildItem(
              index: e.getIndex(),
              icon: e.icon,
              tabName: e.tabName,
            ),
          )
          .toList(),
      onTap: (index) => onSelectTab(
        index,
      ),
    );
  }
  BottomNavigationBarItem _buildItem(
      {required int index, required IconData icon, required String tabName}) {
    return BottomNavigationBarItem(
      icon: Icon(
        icon,
        color: _tabColor(index: index),
      ),
      title: Text(
        tabName,
        style: TextStyle(
          color: _tabColor(index: index),
          fontSize: 12,
        ),
      ),
    );
  }
  Color _tabColor({required int index}) {
    return AppState.currentTab == index
        ? Colors.red
        : Colors.black;
  }
}

TabItem.dart

class TabItem {
  final String tabName;
  final IconData icon;
  final GlobalKey<NavigatorState> key = GlobalKey<NavigatorState>();
  int _index = 0;
  late Widget _page;
  TabItem({
    required this.tabName,
    required this.icon,
    required Widget page,
  }) {
    _page = page;
  }
  void setIndex(int i) {
    _index = i;
  }
  int getIndex() => _index;
  Widget get page {
    return Visibility(
      visible: _index == AppState.currentTab,
      maintainState: true,
      child: Navigator(
        key: key,
        onGenerateRoute: (routeSettings) {
          return MaterialPageRoute(
            builder: (_) => _page,
          );
        },
      ),
    );
  }
}

SearchPage.dart

class SearchPage extends StatefulWidget {
  const SearchPage({Key? key}) : super(key: key);
  @override
  _SearchPageState createState() => _SearchPageState();
}
class _SearchPageState extends State<SearchPage> {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Container(
        child: Center(
          child: TextButton(
            onPressed: () {
              Navigator.of(context).pushReplacement(MaterialPageRoute(
                  builder: (context) => App()));
            },
            child: Text('Switch'),
          ),
        ),
      ),
    );
  }
}