Updating a page every time I revisit the page in BottomNavigationbar

In my app the user is able to store favorite items on a different page in the bottom navigation bar. My problem is that the page does not refresh properly. If you add a favorite it gets displayed only when restarting the app. If the favorites page is in the same widget hierarchy of the respective bottomnavitem the function works fine.

    class Favorites extends StatefulWidget {
  const Favorites({Key? key}) : super(key: key);

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

class _FavoritesState extends State<Favorites> {
  // ignore: prefer_typing_uninitialized_variables
  var database;
  List<Mechanism> people = <Mechanism>[];

  Future initDb() async {
    database = await openDatabase(
      join(await getDatabasesPath(), 'person_database.db'),
      onCreate: (db, version) {
        return db.execute(
          "CREATE TABLE person(id INTEGER PRIMARY KEY,  name TEXT, height TEXT, mass TEXT, hair_color TEXT, skin_color TEXT, eye_color TEXT, birth_year TEXT, gender TEXT)",
        );
      },
      version: 1,
    );

    getPeople().then((value) {
      setState(() {
        people = value;
      });
    });
  }

  Future<List<Mechanism>> getPeople() async {
    final Database db = await database;

    final List<Map<String, dynamic>> maps = await db.query('person');
    return List.generate(maps.length, (i) {
      return Mechanism(
        id: maps[i]['id'],
        name: maps[i]['name'] as String,
      );
    });
  }


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

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      backgroundColor: backGround,
      appBar: AppBar(
        backgroundColor: appbarColor,
        title: const Text("Favorites"),
      ),
      body: ListView.builder(
          itemCount: people.length,
          itemBuilder: (context, index) {
            var person = people[index];
            return ListTile(
              title: Text(
                person.name,
                style: const TextStyle(color: titleColor),
              ),
              onTap: () {
                Navigator.push(
                  context,
                  MaterialPageRoute(
                      builder: (context) =>
                          MechanismDtl(mechanism: person, id: index)),
                );
              },
            );
          }),
    );
  }
}

Edit: page where the user can store the items

class MarkFavs extends StatefulWidget {
  const MarkFavs({Key key}) : super(key: key);

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

class _MarkFavsState extends State<MarkFavs> {
  TextEditingController searchController = TextEditingController();
  List<People> shownList = <People>[
    People(name: 'Test', id: 1),
    People(name: 'Test2', id: 2),
    People(name: 'Test3', id: 3)
  ];
  List<People> initialData = <People>[
    People(name: 'Test', id: 1),
    People(name: 'Test2', id: 2),
    People(name: 'Test3', id: 3)
  ];

  void queryPeople(String queryString) {
    if (kDebugMode) {
      print("queryString = $queryString");
    }

    setState(() {
      shownList = initialData.where((string) {
        if (string.name.toLowerCase().contains(queryString.toLowerCase())) {
          return true;
        } else {
          return false;
        }
      }).toList();
    });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      backgroundColor: backGround,
      appBar: AppBar(
        backgroundColor: appbarColor,
        title: const Text('Detail'),
      ),
      body: Column(
        children: <Widget>[
          TextButton.icon(
            label: const Text('Favorites'),
            icon: const Icon(
              Icons.storage,
              color: titleColor,
            ),
            onPressed: () {
              Navigator.push(
                context,
                MaterialPageRoute(builder: (context) => const Favorites()),
              );
            },
          ),
          Expanded(
            child: PeopleList(
              people: shownList,
            ),
          ),
        ],
      ),
    );
  }
}

class PeopleList extends StatelessWidget {
  final List<People> people;

  const PeopleList({Key key, this.people}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    return ListView.builder(
      itemCount: people.length,
      itemBuilder: (context, index) {
        var person = people[index];
        var name = person.name;
        return ListTile(
          title: Text(
            name,
            style: const TextStyle(color: titleColor),
          ),
          onTap: () {
            person.id = index;
            Navigator.push(
              context,
              MaterialPageRoute(
                  builder: (context) =>
                      MechanismDtl(mechanism: person, id: index)),
            );
          },
        );
      },
    );
  }
}