I encountered the same problem a while ago and came up with my own solution. It may not be exactly what you’re looking for, but it worked perfectly for me.

I use only a list of offsets, which I store the offset of each page being showed

Here is the example app code for you to test if you want:

import 'package:flutter/material.dart';

void main() {
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        colorScheme: ColorScheme.fromSeed(seedColor: Colors.deepPurple),
        useMaterial3: true,
      ),
      home: const MyHomePage(title: 'Flutter Demo Home Page'),
    );
  }
}

class MyHomePage extends StatefulWidget {
  const MyHomePage({super.key, required this.title});

  final String title;

  @override
  State<MyHomePage> createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  int _currentIndex = 0;

  final ScrollController scrollController = ScrollController();
  List<double> offsets = [];

  @override
  void initState() {
    // Number of options in the bottomNavigationBar
    offsets.addAll([0, 0, 0]);
    super.initState();
  }

  final List<Widget> _pages = [
    SingleChildScrollView(
      child: Column(
        children: List.generate(
            20, (index) => ListTile(title: Text('Home Item $index'))),
      ),
    ),
    SingleChildScrollView(
      child: Column(
        children: List.generate(
            20, (index) => ListTile(title: Text('Search Item $index'))),
      ),
    ),
    SingleChildScrollView(
      child: Column(
        children: List.generate(
            20, (index) => ListTile(title: Text('Profile Item $index'))),
      ),
    ),
  ];

  void _scrollToTop() {
    scrollController.jumpTo(0);
  }

  void _onTabTapped(int index) {
    // Select the offset for the selected page
    offsets[_currentIndex] = scrollController.offset;
    setState(() {
      _currentIndex = index;
      scrollController.jumpTo(offsets[index]);
    });
  }

  @override
  Widget build(BuildContext context) {
    return PrimaryScrollController(
      controller: scrollController,
      child: Scaffold(
        appBar: AppBar(
          title: Text('BottomNavigationBar + Scroll'),
        ),
        body: _pages[_currentIndex],
        bottomNavigationBar: BottomNavigationBar(
          currentIndex: _currentIndex,
          onTap: _onTabTapped,
          items: [
            BottomNavigationBarItem(
              icon: Icon(Icons.home),
              label: 'Home',
            ),
            BottomNavigationBarItem(
              icon: Icon(Icons.search),
              label: 'Search',
            ),
            BottomNavigationBarItem(
              icon: Icon(Icons.person),
              label: 'Profile',
            ),
          ],
        ),
        floatingActionButton: Column(
          mainAxisAlignment: MainAxisAlignment.end,
          children: [
            FloatingActionButton(
              onPressed: _scrollToTop,
              child: Icon(Icons.arrow_upward),
              tooltip: 'Scroll to Top',
            ),
          ],
        ),
      ),
    );
  }
}