Flutter what is the best way to design a form with a button on bottom?

I have been searching for so long to find a good solution to my problem. I want to have this layout:

So far I have managed to do this:

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

  @override
  State<FormPage> createState() => _FormPageState();
}

class _FormPageState extends State<FormPage> {
  bool hasManyData = false;

  // List of many data
  final List<String> dataLong = List.generate(20, (index) => "Data $index");

  // List of few data
  final List<String> dataShort = List.generate(2, (index) => "Data $index");

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: SafeArea(
        child: Column(
          children: [
            ElevatedButton(
              onPressed: () {
                setState(() {
                  hasManyData = !hasManyData;
                });
              },
              child: const Text("change Data Size"),
            ),
            Expanded(
              child: SingleChildScrollView(
                child: Column(
                  children: [
                    for (final data in hasManyData ? dataLong : dataShort)
                      ListTile(
                        title: Text(data),
                      ),
                    const TextField(
                      decoration: InputDecoration(
                        hintText: "Name",
                      ),
                    ),
                    ElevatedButton(
                      onPressed: () {},
                      child: const Text("Submit"),
                    ),
                  ],
                ),
              ),
            ),
          ],
        ),
      ),
    );
  }
}

Which is almost the same but the submit button is not on the bottom when there are few data (you can change data size using the button).

Every way that I have tried so many things with Slivers and without always there was something breaking, I want to keep the keyboard functionality as is without overflowing or the Submit button moving up with the keyboard.

EDIT:
I have managed to do that:

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

  @override
  State<FormPage> createState() => _FormPageState();
}

class _FormPageState extends State<FormPage> {
  bool hasManyData = false;

  // List of many data
  final List<String> dataLong = List.generate(20, (index) => "Data $index");

  // List of few data
  final List<String> dataShort = List.generate(2, (index) => "Data $index");

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: SafeArea(
        child: Column(
          children: [
            ElevatedButton(
              onPressed: () {
                setState(() {
                  hasManyData = !hasManyData;
                });
              },
              child: const Text("change Data Size"),
            ),
            Expanded(
              child: CustomScrollView(
                slivers: [
                  SliverFillRemaining(
                    hasScrollBody: false,
                    child: Column(
                      crossAxisAlignment: CrossAxisAlignment.start,
                      children: [
                        for (final data in hasManyData ? dataLong : dataShort)
                          ListTile(
                            title: Text(data),
                          ),
                        const TextField(
                          decoration: InputDecoration(
                            hintText: "Name",
                          ),
                        ),
                        const Spacer(),
                        ElevatedButton(
                          onPressed: () {},
                          child: const Text("Submit"),
                        ),
                      ],
                    ),
                  ),
                ],
              ),
            ),
          ],
        ),
      ),
    );
  }
}

But now the submit button gets pushed up when the keyboard opens, and hiding the button when the keyboard opens is an option… but a very bad one imo because it takes a second for it to reapear.