feat: implement Iteration 0 foundation (backend + Flutter client)

Backend (Go):
- Project structure with chi router, pgxpool, goose migrations
- JWT auth (access/refresh tokens) with Firebase token verification
- NoopTokenVerifier for local dev without Firebase credentials
- PostgreSQL user repository with atomic profile updates (transactions)
- Mifflin-St Jeor calorie calculation based on profile data
- REST API: POST /auth/login, /auth/refresh, /auth/logout, GET/PUT /profile, GET /health
- Middleware: auth, CORS (localhost wildcard), logging, recovery, request_id
- Unit tests (51 passing) and integration tests (testcontainers)
- Docker Compose setup with postgres healthcheck and graceful shutdown

Flutter client:
- Riverpod state management with GoRouter navigation
- Firebase Auth (email/password + Google sign-in with web popup support)
- Platform-aware API URLs (web/Android/iOS)
- Dio HTTP client with JWT auth interceptor and concurrent refresh handling
- Secure token storage
- Screens: Login, Register, Home (tabs: Menu, Recipes, Products, Profile)
- Unit tests (17 passing)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

client/test/features/auth/register_screen_test.dart

@@ -0,0 +1,111 @@
+import 'package:flutter/material.dart';
+import 'package:flutter_riverpod/flutter_riverpod.dart';
+import 'package:flutter_test/flutter_test.dart';
+import 'package:go_router/go_router.dart';
+
+import 'package:food_ai/core/auth/auth_provider.dart';
+import 'package:food_ai/features/auth/register_screen.dart';
+
+class _TestAuthNotifier extends AuthNotifier {
+  _TestAuthNotifier()
+      : super.test(const AuthState(status: AuthStatus.unauthenticated));
+
+  @override
+  Future<void> signInWithEmail(String email, String password) async {}
+
+  @override
+  Future<void> signInWithGoogle() async {}
+
+  @override
+  Future<void> register(String email, String password, String name) async {}
+
+  @override
+  Future<void> signOut() async {}
+}
+
+Widget _buildTestWidget() {
+  final router = GoRouter(
+    initialLocation: '/auth/register',
+    routes: [
+      GoRoute(
+        path: '/auth/register',
+        builder: (_, __) => const RegisterScreen(),
+      ),
+      GoRoute(
+        path: '/auth/login',
+        builder: (_, __) =>
+            const Scaffold(body: Text('Login Screen')),
+      ),
+      GoRoute(
+        path: '/home',
+        builder: (_, __) =>
+            const Scaffold(body: Text('Home Screen')),
+      ),
+    ],
+  );
+
+  return ProviderScope(
+    overrides: [
+      authProvider.overrideWith(
+        (ref) => _TestAuthNotifier(),
+      ),
+    ],
+    child: MaterialApp.router(routerConfig: router),
+  );
+}
+
+void main() {
+  testWidgets('renders all form fields', (tester) async {
+    await tester.pumpWidget(_buildTestWidget());
+    await tester.pumpAndSettle();
+
+    expect(find.text('Имя'), findsOneWidget);
+    expect(find.text('Email'), findsOneWidget);
+    expect(find.text('Пароль'), findsOneWidget);
+    expect(find.text('Подтверждение пароля'), findsOneWidget);
+    expect(find.text('Зарегистрироваться'), findsOneWidget);
+  });
+
+  testWidgets('validates empty name', (tester) async {
+    await tester.pumpWidget(_buildTestWidget());
+    await tester.pumpAndSettle();
+
+    await tester.tap(find.text('Зарегистрироваться'));
+    await tester.pumpAndSettle();
+
+    expect(find.text('Введите имя'), findsOneWidget);
+  });
+
+  testWidgets('validates password mismatch', (tester) async {
+    await tester.pumpWidget(_buildTestWidget());
+    await tester.pumpAndSettle();
+
+    await tester.enterText(
+        find.widgetWithText(TextFormField, 'Имя'), 'Test');
+    await tester.enterText(
+        find.widgetWithText(TextFormField, 'Email'), 'test@test.com');
+    await tester.enterText(
+        find.widgetWithText(TextFormField, 'Пароль'), 'password123');
+    await tester.enterText(
+        find.widgetWithText(TextFormField, 'Подтверждение пароля'),
+        'different');
+    await tester.tap(find.text('Зарегистрироваться'));
+    await tester.pumpAndSettle();
+
+    expect(find.text('Пароли не совпадают'), findsOneWidget);
+  });
+
+  testWidgets('has link to login', (tester) async {
+    await tester.pumpWidget(_buildTestWidget());
+    await tester.pumpAndSettle();
+
+    expect(find.text('Уже есть аккаунт? Войти'), findsOneWidget);
+  });
+
+  testWidgets('shows registration title', (tester) async {
+    await tester.pumpWidget(_buildTestWidget());
+    await tester.pumpAndSettle();
+
+    expect(find.text('Регистрация'), findsOneWidget);
+  });
+}