How to trigger dispose from another page - firebase

Question

I have two pages, Page_1 which uses didChangeAppLifecycleState which looks out for when the user closes the app. While the user is on the app, a timer increases, as soon as the user closes the app, the timer stops.
Page_2 has a logout button, which uses firebase signOut() function.
If I were to use the logout function in Page_1 and sign in with another account, the timer would start new for the second user, but If I were to logout from my Page_2 and sign in with another user, then the timer would of carried from the first user instead of starting again,
What I'm asking is how can I use WidgetsBinding.instance!.removeObserver(this); on Page_2 instead of Page_1
Page_1.dart
class _HomeScreenState extends State<HomeScreen> with WidgetsBindingObserver {
User? user = FirebaseAuth.instance.currentUser;
UserModel loggedInUser = UserModel();
final _auth = FirebaseAuth.instance;
StreamController<int> controller = StreamController();
late StreamSubscription<int> streamSubscription;
#override
void initState() {
super.initState();
WidgetsBinding.instance!.addObserver(this);
print(user!.uid);
FirebaseFirestore.instance
.collection("users")
.doc(user!.uid)
.get()
.then((value) {
loggedInUser = UserModel.fromMap(value.data());
setState(() {});
});
app_start = DateTime.now();
}
late DateTime app_start;
late DateTime app_end;
#override
void didChangeAppLifecycleState(AppLifecycleState state) {
super.didChangeAppLifecycleState(state);
print(state);
// if user clicks logout end this funciton
// Checks if app is active
final isBackground = state == AppLifecycleState.paused;
if (state == AppLifecycleState.inactive ||
state == AppLifecycleState.detached) return;
if (isBackground) {
FirebaseFirestore.instance
.collection("users")
.doc(user!.uid)
.get()
.then((value) {
loggedInUser = UserModel.fromMap(value.data());
if (loggedInUser.timeActive == null) {
loggedInUser.timeActive = 1;
} else {
}
app_end = DateTime.now();
final differenceInDays = app_end.difference(app_start).inSeconds;
int? test = loggedInUser.timeActive;
int? totalOnTime = differenceInDays + loggedInUser.timeActive!.toInt();
FirebaseFirestore.instance
.collection('users')
.doc(loggedInUser.uid)
.update({"timeActive": totalOnTime});
setState(() {});
});
} else {
app_start = DateTime.now();
}
}
#override
void dispose() {
// TODO: implement dispose
super.dispose();
WidgetsBinding.instance!.removeObserver(this);
}
}
Page_2.dart
#override
void dispose() {
// TODO: implement dispose
super.dispose();
WidgetsBinding.instance!.removeObserver(this);
}
ElevatedButton(
onPressed: () {
dispose()
_auth.signOut();
Navigator.of(context).pushReplacement(
MaterialPageRoute(
builder: (context) =>
LoginScreen()));
print("clicked");
},
child: Text('Log out'),
)