Add app source and tests

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

test/widget_test.dart

@@ -0,0 +1,13 @@
+import 'package:flutter/material.dart';
+import 'package:flutter_test/flutter_test.dart';
+
+import 'package:peach/main.dart';
+
+void main() {
+  testWidgets('Peach shows the branded splash on boot', (tester) async {
+    await tester.pumpWidget(const Peach());
+    // While storage loads, the splash screen is shown.
+    expect(find.text('Peach'), findsOneWidget);
+    expect(find.byType(LinearProgressIndicator), findsWidgets);
+  });
+}