Flutter – Why would a widget rebuild in its parent file but not rebuild when placed in a separate file?

I’m using the gsheets package to asynchronously read and write data to a Google spreadsheet. I click a button on an AppBar() on the home page to add a row to the database. The row is successfully added to the spreadsheet. Here is the code:

// import statements

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

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

class _HomePageState extends State<HomePage> {
  bool viewNotebooks = false;
  bool viewList = true;

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        leadingWidth: 650,
        leading: Row(
          mainAxisAlignment: MainAxisAlignment.start,
          children: [
            // code irrelevant to this question, then
            TextButton.icon(
                icon: const Icon(Icons.note_add_outlined),
                label: const Text("New Note"),
                onPressed: () async {
                  await Data.addNote(
                      title: 'New Note', content: '[content goes here]');
                  setState(() {});
                }),
            // more code 
          ],
        ),
      ),
      body: Row(
        children: [
          // more code
          viewList
              ? const Expanded(
                  flex: 1,
                  child: NotesListView(),
                )
              : Container(),
          // more code
        ],
      ),
    );
  }
}

A ListView.builder() should then rebuild to include the new row’s data in its items. Here is the relevant code, in a separate .dart file:

import 'package:flutter/material.dart';
import '../providers/sheets_api.dart';

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

  @override
  State<NotesListView> createState() => _NotesListViewState();
}

class _NotesListViewState extends State<NotesListView> {
  @override
  Widget build(BuildContext context) {
    return FutureBuilder(
      future: Data.getRows(),
      builder: (context, snapshot) {
        if (snapshot.connectionState == ConnectionState.waiting) {
          return const Center(
           child: CircularProgressIndicator(),
         );
        }
        if (snapshot.hasData) {
          return ListView.builder(
            shrinkWrap: true,
            itemCount: snapshot.data!.length,
            itemBuilder: (context, index) {
              return ListTile(
                  title: Text(snapshot.data![index][1]),
                  subtitle: Text(snapshot.data![index][2]),
                  onTap: () async {
                    var id = snapshot.data![index][0];
                    // print(await Data.getNoteById(id));
                  });
            },
          );
       } else {
          return const Center(
            // render the loading indicator
           child: CircularProgressIndicator(),
          );
        }
      },
    );
  }
}

The widget, however, does not rebuild when the spreadsheet content changes. But when I put the code in the app’s main.dart file, even in a widget outside _NotesListViewState, the UI does rebuild as expected.

Widget notesListView() {
  return FutureBuilder (
  // rest of code

I’m struggling to understand what’s going on. I’ve read about BuildContexts and widget trees, and about keys, and I assume it’s something about the BuildContext for NotesListView being outside the main app’s widget tree? But I don’t really understand and, if that’s the case, I don’t know how to have NotesListView be separate (with its own BuildContext) and yet still be seen within the main app’s context. I know I could use something like Provider to control when widgets rebuild, or just keep the custom notesListView widget in HomePage, but I’d like to understand what’s going on here.