Keep the text inputs values when changing the layout

main.dart

import 'package:flutter/material.dart';

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

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

  @override
  Widget build(BuildContext context) {
    return const MaterialApp(title: 'Playground', home: MyHomePage());
  }
}

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

  @override
  Widget build(BuildContext context) {
    final TextEditingController controller = TextEditingController();

    return Scaffold(
      appBar: AppBar(title: const Text("Playground")),
      body: ResponsiveBuilder(
        small: Column(
          children: [
            const Text("Small"),
            Center(
              child: SizedBox(
                width: 200,
                child: TextField(
                  controller: controller,
                  decoration: const InputDecoration(
                    hintText: 'Small screen hint',
                  ),
                ),
              ),
            ),
          ],
        ),
        large: Column(
          children: [
            const Text("Large"),
            Container(
              constraints: const BoxConstraints(maxWidth: 400),
              child: TextField(
                controller: controller,
                decoration: const InputDecoration(
                  hintText: 'Large screen hint',
                ),
              ),
            ),
          ],
        ),
      ),
    );
  }
}

class ResponsiveBuilder extends StatelessWidget {
  const ResponsiveBuilder({
    Key? key,
    required this.small,
    required this.large,
  }) : super(key: key);

  final Widget small;
  final Widget large;

  @override
  Widget build(BuildContext context) {
    if (MediaQuery.of(context).size.width > 650) return large;

    return small;
  }
}