Compartilhando código do desafio

Testando apenas o widget icon_picker.dart:

  testWidgets(
    'Open IconPicker and find an icon',
    (tester) async {
      await tester.pumpWidget(MaterialApp(
        home: Builder(
          builder: (context) => TextButton(
              onPressed: () async => await showIconPicker(context: context),
              child: const Text('Open icon picker')),
        ),
      ));

      await tester.tap(find.byType(TextButton));
      await tester.pumpAndSettle();
      expect(find.byIcon(Icons.card_giftcard), findsOneWidget);
    },
  );

Testando a ação de deletar o cliente:

 expect(find.text('Dandara (Ferro)'), findsOneWidget);

      //Testando deletar o cliente
      await tester.drag(find.text('Dandara (Ferro)'), const Offset(500, 0));
      await tester.pumpAndSettle();
      expect(find.text('Dandara (Ferro)'), findsNothing);

Testando a ação de sair do app:

//Saindo do app
      await tester.tap(find.byIcon(Icons.menu));
      await tester.pumpAndSettle();
      await tester.tap(find.text('Sair'));