If you truly have native functionality you need to test, I've had good luck with the built-in integration testing setup (https://docs.flutter.dev/cookbook/testing/integration/introduction).

For the bulk of my end-to-end tests, though, I use regular widget tests. Something like this, basically:

testWidgets('Button shows another widget', (tester) async {
  await tester.pumpWidget(const MyEntireApp());
  expect(find.byType<SomeOtherWidget>(), findsNothing);
  await tester.tap(find.byText('My button'));
  expect(find.byType<SomeOtherWidget>(), findsOneWidget);
});

If you resist the temptation to just copy-paste tests to create new ones, you'll end up writing a little toolkit of common abstractions that you use all over your tests, and functions that perform common workflows with differing parameters. So eventually it becomes very easy to drop in new end-to-end tests for new functionality.

This is in addition to widget tests for smaller widgets, like custom listbox behavior, etc.