feat(01-02): create router, navigation shell, screens, and app shell test

- GoRouter with StatefulShellRoute.indexedStack and 3 branches (Home, Rooms, Settings)
- AppShell with NavigationBar using localized labels and thematic icons
- HomeScreen with empty state and cross-navigation to Rooms tab
- RoomsScreen with empty state and placeholder action button
- SettingsScreen with SegmentedButton theme switcher and About section
- Widget test verifying 3 navigation destinations with correct German labels

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

lib/core/router/router.dart

@@ -0,0 +1,42 @@
+import 'package:go_router/go_router.dart';
+
+import 'package:household_keeper/features/home/presentation/home_screen.dart';
+import 'package:household_keeper/features/rooms/presentation/rooms_screen.dart';
+import 'package:household_keeper/features/settings/presentation/settings_screen.dart';
+import 'package:household_keeper/shell/app_shell.dart';
+
+final router = GoRouter(
+  initialLocation: '/',
+  routes: [
+    StatefulShellRoute.indexedStack(
+      builder: (context, state, navigationShell) =>
+          AppShell(navigationShell: navigationShell),
+      branches: [
+        StatefulShellBranch(
+          routes: [
+            GoRoute(
+              path: '/',
+              builder: (context, state) => const HomeScreen(),
+            ),
+          ],
+        ),
+        StatefulShellBranch(
+          routes: [
+            GoRoute(
+              path: '/rooms',
+              builder: (context, state) => const RoomsScreen(),
+            ),
+          ],
+        ),
+        StatefulShellBranch(
+          routes: [
+            GoRoute(
+              path: '/settings',
+              builder: (context, state) => const SettingsScreen(),
+            ),
+          ],
+        ),
+      ],
+    ),
+  ],
+);

lib/features/home/presentation/home_screen.dart

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+import 'package:flutter/material.dart';
+import 'package:go_router/go_router.dart';
+
+import 'package:household_keeper/l10n/app_localizations.dart';
+
+class HomeScreen extends StatelessWidget {
+  const HomeScreen({super.key});
+
+  @override
+  Widget build(BuildContext context) {
+    final l10n = AppLocalizations.of(context);
+    final theme = Theme.of(context);
+
+    return Center(
+      child: Padding(
+        padding: const EdgeInsets.symmetric(horizontal: 32),
+        child: Column(
+          mainAxisSize: MainAxisSize.min,
+          children: [
+            Icon(
+              Icons.checklist_rounded,
+              size: 80,
+              color: theme.colorScheme.onSurface.withValues(alpha: 0.4),
+            ),
+            const SizedBox(height: 24),
+            Text(
+              l10n.homeEmptyTitle,
+              style: theme.textTheme.headlineSmall,
+              textAlign: TextAlign.center,
+            ),
+            const SizedBox(height: 8),
+            Text(
+              l10n.homeEmptyMessage,
+              style: theme.textTheme.bodyLarge?.copyWith(
+                color: theme.colorScheme.onSurface.withValues(alpha: 0.6),
+              ),
+              textAlign: TextAlign.center,
+            ),
+            const SizedBox(height: 24),
+            FilledButton.tonal(
+              onPressed: () => context.go('/rooms'),
+              child: Text(l10n.homeEmptyAction),
+            ),
+          ],
+        ),
+      ),
+    );
+  }
+}

lib/features/rooms/presentation/rooms_screen.dart

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+import 'package:flutter/material.dart';
+
+import 'package:household_keeper/l10n/app_localizations.dart';
+
+class RoomsScreen extends StatelessWidget {
+  const RoomsScreen({super.key});
+
+  @override
+  Widget build(BuildContext context) {
+    final l10n = AppLocalizations.of(context);
+    final theme = Theme.of(context);
+
+    return Center(
+      child: Padding(
+        padding: const EdgeInsets.symmetric(horizontal: 32),
+        child: Column(
+          mainAxisSize: MainAxisSize.min,
+          children: [
+            Icon(
+              Icons.door_front_door_rounded,
+              size: 80,
+              color: theme.colorScheme.onSurface.withValues(alpha: 0.4),
+            ),
+            const SizedBox(height: 24),
+            Text(
+              l10n.roomsEmptyTitle,
+              style: theme.textTheme.headlineSmall,
+              textAlign: TextAlign.center,
+            ),
+            const SizedBox(height: 8),
+            Text(
+              l10n.roomsEmptyMessage,
+              style: theme.textTheme.bodyLarge?.copyWith(
+                color: theme.colorScheme.onSurface.withValues(alpha: 0.6),
+              ),
+              textAlign: TextAlign.center,
+            ),
+            const SizedBox(height: 24),
+            FilledButton.tonal(
+              onPressed: () {
+                // Room creation will be implemented in Phase 2
+              },
+              child: Text(l10n.roomsEmptyAction),
+            ),
+          ],
+        ),
+      ),
+    );
+  }
+}

lib/features/settings/presentation/settings_screen.dart

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+import 'package:flutter/material.dart';
+import 'package:flutter_riverpod/flutter_riverpod.dart';
+
+import 'package:household_keeper/core/theme/theme_provider.dart';
+import 'package:household_keeper/l10n/app_localizations.dart';
+
+class SettingsScreen extends ConsumerWidget {
+  const SettingsScreen({super.key});
+
+  @override
+  Widget build(BuildContext context, WidgetRef ref) {
+    final l10n = AppLocalizations.of(context);
+    final theme = Theme.of(context);
+    final currentThemeMode = ref.watch(themeProvider);
+
+    return ListView(
+      children: [
+        // Section 1: Appearance (Darstellung)
+        Padding(
+          padding: const EdgeInsets.fromLTRB(16, 24, 16, 8),
+          child: Text(
+            l10n.settingsSectionAppearance,
+            style: theme.textTheme.titleMedium?.copyWith(
+              color: theme.colorScheme.primary,
+            ),
+          ),
+        ),
+        ListTile(
+          title: Text(l10n.settingsThemeLabel),
+          subtitle: Padding(
+            padding: const EdgeInsets.only(top: 8),
+            child: SegmentedButton<ThemeMode>(
+              segments: [
+                ButtonSegment<ThemeMode>(
+                  value: ThemeMode.system,
+                  label: Text(l10n.themeSystem),
+                  icon: const Icon(Icons.settings_suggest_outlined),
+                ),
+                ButtonSegment<ThemeMode>(
+                  value: ThemeMode.light,
+                  label: Text(l10n.themeLight),
+                  icon: const Icon(Icons.light_mode_outlined),
+                ),
+                ButtonSegment<ThemeMode>(
+                  value: ThemeMode.dark,
+                  label: Text(l10n.themeDark),
+                  icon: const Icon(Icons.dark_mode_outlined),
+                ),
+              ],
+              selected: {currentThemeMode},
+              onSelectionChanged: (selection) {
+                ref
+                    .read(themeProvider.notifier)
+                    .setThemeMode(selection.first);
+              },
+            ),
+          ),
+        ),
+
+        const Divider(indent: 16, endIndent: 16, height: 32),
+
+        // Section 2: About (Ueber)
+        Padding(
+          padding: const EdgeInsets.fromLTRB(16, 8, 16, 8),
+          child: Text(
+            l10n.settingsSectionAbout,
+            style: theme.textTheme.titleMedium?.copyWith(
+              color: theme.colorScheme.primary,
+            ),
+          ),
+        ),
+        ListTile(
+          title: Text(l10n.aboutAppName),
+          subtitle: Text(l10n.aboutTagline),
+        ),
+        ListTile(
+          title: const Text('Version'),
+          subtitle: Text(l10n.aboutVersion('0.1.0')),
+        ),
+      ],
+    );
+  }
+}

lib/shell/app_shell.dart

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+import 'package:flutter/material.dart';
+import 'package:go_router/go_router.dart';
+
+import 'package:household_keeper/l10n/app_localizations.dart';
+
+class AppShell extends StatelessWidget {
+  const AppShell({
+    required this.navigationShell,
+    super.key,
+  });
+
+  final StatefulNavigationShell navigationShell;
+
+  @override
+  Widget build(BuildContext context) {
+    final l10n = AppLocalizations.of(context);
+
+    return Scaffold(
+      body: navigationShell,
+      bottomNavigationBar: NavigationBar(
+        selectedIndex: navigationShell.currentIndex,
+        onDestinationSelected: (index) {
+          navigationShell.goBranch(
+            index,
+            initialLocation: index == navigationShell.currentIndex,
+          );
+        },
+        destinations: [
+          NavigationDestination(
+            icon: const Icon(Icons.checklist_outlined),
+            selectedIcon: const Icon(Icons.checklist),
+            label: l10n.tabHome,
+          ),
+          NavigationDestination(
+            icon: const Icon(Icons.door_front_door_outlined),
+            selectedIcon: const Icon(Icons.door_front_door),
+            label: l10n.tabRooms,
+          ),
+          NavigationDestination(
+            icon: const Icon(Icons.tune_outlined),
+            selectedIcon: const Icon(Icons.tune),
+            label: l10n.tabSettings,
+          ),
+        ],
+      ),
+    );
+  }
+}

test/shell/app_shell_test.dart

@@ -0,0 +1,70 @@
+import 'package:flutter/material.dart';
+import 'package:flutter_riverpod/flutter_riverpod.dart';
+import 'package:flutter_test/flutter_test.dart';
+import 'package:shared_preferences/shared_preferences.dart';
+
+import 'package:household_keeper/core/router/router.dart';
+import 'package:household_keeper/l10n/app_localizations.dart';
+
+void main() {
+  group('AppShell Navigation', () {
+    setUp(() {
+      SharedPreferences.setMockInitialValues({});
+    });
+
+    testWidgets('renders 3 navigation destinations with correct German labels',
+        (tester) async {
+      await tester.pumpWidget(
+        ProviderScope(
+          child: MaterialApp.router(
+            routerConfig: router,
+            localizationsDelegates: AppLocalizations.localizationsDelegates,
+            supportedLocales: const [Locale('de')],
+            locale: const Locale('de'),
+          ),
+        ),
+      );
+      await tester.pumpAndSettle();
+
+      // Verify 3 NavigationDestination widgets are rendered
+      expect(find.byType(NavigationDestination), findsNWidgets(3));
+
+      // Verify correct German labels from ARB (with umlauts)
+      expect(find.text('\u00dcbersicht'), findsOneWidget);
+      expect(find.text('R\u00e4ume'), findsOneWidget);
+      expect(find.text('Einstellungen'), findsOneWidget);
+    });
+
+    testWidgets('tapping a destination changes the selected tab',
+        (tester) async {
+      await tester.pumpWidget(
+        ProviderScope(
+          child: MaterialApp.router(
+            routerConfig: router,
+            localizationsDelegates: AppLocalizations.localizationsDelegates,
+            supportedLocales: const [Locale('de')],
+            locale: const Locale('de'),
+          ),
+        ),
+      );
+      await tester.pumpAndSettle();
+
+      // Initially on Home tab (index 0) -- verify home empty state is shown
+      expect(find.text('Noch nichts zu tun!'), findsOneWidget);
+
+      // Tap the Rooms tab (second destination)
+      await tester.tap(find.text('R\u00e4ume'));
+      await tester.pumpAndSettle();
+
+      // Verify we see Rooms content now
+      expect(find.text('Hier ist noch alles leer!'), findsOneWidget);
+
+      // Tap the Settings tab (third destination)
+      await tester.tap(find.text('Einstellungen'));
+      await tester.pumpAndSettle();
+
+      // Verify we see Settings content now
+      expect(find.text('Darstellung'), findsOneWidget);
+    });
+  });
+}