how do i instantly update a value in appbar in flutter

Calling [setState] notifies the framework that the internal state of
this object has changed in a way that might impact the user interface
in this subtree, which causes the framework to schedule a [build] for
this [State] object.

The key is rebuild your widgets tree everytime you change your widget’ states

When you do like this

class Page1 extends StatefulWidget {
  UserInfos userInfo;

  const Page1({super.key, required this.userInfo});

  @override
  State<Page1> createState() => _Page1State();
}

class _Page1State extends State<Page1> {
  @override
  Widget build(BuildContext context) {
    return Center(
      child: ElevatedButton(
          onPressed: () {
            setState(() { // Page1 state changed, not homepage state
              widget.userInfo.money -= 1;
            });
          },
          child: const Text('decrease money')),
    );
  }
}

only page1 widget will be scheduled to rebuild. If you want to update changes to your homepage widget, you need to call setState inside your homepage widget

class HomePage extends StatefulWidget {
  const HomePage({super.key});

  @override
  State<HomePage> createState() => _HomePageState();
}

class _HomePageState extends State<HomePage> {

  UserInfos _userInfo = new UserInfos();

  // setState here when userInfos changed

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(title: Text(_userInfo.money.toString())),
      body: PageView(
        children: [
          Page1(userInfo: _userInfo),
          Page2(userInfo: _userInfo),
        ],
      ),
    );
  }
}

There are many way to do this, the simplest is callback.

Your HomePage widget:

class HomePage extends StatefulWidget {
  const HomePage({super.key});

  @override
  State<HomePage> createState() => _HomePageState();
}

class _HomePageState extends State<HomePage> {
  void _updateState() {
    setState(() {
      UserInfo.money += 100;
    });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(title: Text(UserInfo.money.toString())),
      body: PageView(
        children: List.generate(
          3,
          (index) => Page(
            action: 'Action $index',
            onPressed: _updateState, // Pass your actions to child widget
          ),
        ),
      ),
    );
  }
}

Your Page widget:

class Page extends StatefulWidget {
  const Page({
    super.key,
    required this.action,
    this.onPressed,
  });

  final String action;
  final Function()? onPressed;

  @override
  State<Page> createState() => _PageState();
}

class _PageState extends State<Page> {
  @override
  Widget build(BuildContext context) {
    return Center(
      child: ElevatedButton(
        onPressed: widget.onPressed, // Callback to change state
        child: Text(widget.action),
      ),
    );
  }
}

Your _updateState() function is called inside HomePage widget, so it will rebuild your widget after state changed.

A better way is make your state observable

class UserInfo {
  // when you change money value, every listeners of this will be updated.
  static ValueNotifier<int> money = ValueNotifier(25000);
}

Update money value by

UserInfo.money.value = 100; // new value

And make your appbar listen for money value changes

AppBar(
  title: ValueListenableBuilder( // Your appbar will listen any UserInfo.money change
    valueListenable: UserInfo.money,
    builder: (context, value, child) => Text(value.toString()),
  ),
)

Full solution

import 'package:flutter/material.dart';

class HomePage extends StatefulWidget {
  const HomePage({super.key});

  @override
  State<HomePage> createState() => _HomePageState();
}

class _HomePageState extends State<HomePage> {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: ValueListenableBuilder( // Your appbar will listen any UserInfo.money change
          valueListenable: UserInfo.money,
          builder: (context, value, child) => Text(value.toString()),
        ),
      ),
      body: PageView(
        children: List.generate(
          3,
          (index) => Page(
            action: 'Action $index',
          ),
        ),
      ),
    );
  }
}

class UserInfo {
  static ValueNotifier<int> money = ValueNotifier(25000);
}

class Page extends StatefulWidget {
  const Page({
    super.key,
    required this.action,
  });

  final String action;

  @override
  State<Page> createState() => _PageState();
}

class _PageState extends State<Page> {
  @override
  Widget build(BuildContext context) {
    return Center(
      child: ElevatedButton(
        onPressed: () {
          UserInfo.money.value += 100;
        },
        child: Text(widget.action),
      ),
    );
  }
}