AppBar in Flutter

Hello everyone, I would like to know how I could work in the part that is enclosed, since when creating an AppBar, the one in Green is created. I want to work on the blue without affecting the NavigationDrawer when the other screens are open. I don't know if I should change the NavigationDrawer, or the way I open the screens, since I don't want it to look spliced ​​like in the First Image.

This is the screen shown in the first image

import 'package:flutter/material.dart';

class principal extends StatelessWidget {
  @override
  Widget build(BuildContext context) => Scaffold(
        appBar: AppBar(
          title: Text('Menu'),
          centerTitle: true,
          backgroundColor: Colors.green,
        ),
      );
}

This is the NavigationDrawer

import 'package:flutter/material.dart';
import 'package:flutter_application_1/acercade.dart';
import 'package:flutter_application_1/principal.dart';
import 'corarioch.dart';
import 'corariog.dart';

class Home extends StatefulWidget {
  HomeState createState() => HomeState();
}

class HomeState extends State<Home> {
  int _selectDrawerItem = 0;

  _getDrawerItemWidget(int pos) {
    switch (pos) {
      case 0:
        return principal();
      case 1:
        return corariog();
      case 2:
        return corarioch();
      case 3:
        return acercade();
    }
  }

  _onSelectItem(int pos) {
    Navigator.of(context).pop();
    setState(() {
      _selectDrawerItem = pos;
    });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(),
      drawer: Drawer(
        child: ListView(
          children: <Widget>[
            UserAccountsDrawerHeader(
              accountName: Row(
                mainAxisAlignment: MainAxisAlignment.start,
                children: [
                  Text(
                    "PIBEDS",
                    style: TextStyle(
                        color: Theme.of(context).colorScheme.onPrimary),
                  ),
                ],
              ),
              accountEmail: Row(
                mainAxisAlignment: MainAxisAlignment.start,
                children: [
                  Text(
                    'Cantos de la Iglesia',
                    style: TextStyle(
                        color: Theme.of(context).colorScheme.onPrimary),
                  ),
                ],
              ),
              currentAccountPicture: Row(
                mainAxisAlignment: MainAxisAlignment.start,
                children: [
                  CircleAvatar(
                      backgroundImage: AssetImage('assets/pibedslogopng.png'),
                      radius: 35),
                ],
              ),
            ),
            const SizedBox(height: 15),
            ListTile(
              title: Text('Home'),
              leading: Icon(Icons.home),
              selected: (0 == _selectDrawerItem),
              onTap: () {
                _onSelectItem(0);
              },
            ),
            const SizedBox(height: 15),
            ListTile(
              title: Text('Corario Grande'),
              leading: Icon(Icons.book),
              selected: (1 == _selectDrawerItem),
              onTap: () {
                _onSelectItem(1);
              },
            ),
            const SizedBox(height: 15),
            ListTile(
              title: Text('Corario Chico'),
              leading: Icon(Icons.book),
              selected: (2 == _selectDrawerItem),
              onTap: () {
                _onSelectItem(2);
              },
            ),
            Divider(),
            const SizedBox(height: 15),
            ListTile(
              title: Text('Acerca de'),
              leading: Icon(Icons.info),
              selected: (3 == _selectDrawerItem),
              onTap: () {
                _onSelectItem(3);
              },
            ),
          ],
        ),
      ),
      body: _getDrawerItemWidget(_selectDrawerItem),
    );
  }
}

Second Screen

In this one I also want to work on the blue part without affecting the first screen, since I will be doing different things with the different screens.