feat: implement Iteration 3 — product/receipt/dish recognition

Backend:
- gemini/client.go: refactor to shared callGroq transport; add
  generateVisionContent using llama-3.2-11b-vision-preview model
- gemini/recognition.go: RecognizeReceipt, RecognizeProducts,
  RecognizeDish (vision), ClassifyIngredient (text); shared parseJSON helper
- ingredient/repository.go: add FuzzyMatch (wraps Search, returns best hit)
- recognition/handler.go: POST /ai/recognize-receipt, /ai/recognize-products,
  /ai/recognize-dish; enrichItems with fuzzy match + AI classify fallback;
  parallel multi-image processing with deduplication
- server.go + main.go: wire recognition handler under /ai routes

Flutter:
- pubspec.yaml: add image_picker ^1.1.0
- AndroidManifest.xml: add CAMERA and READ_EXTERNAL_STORAGE permissions
- Info.plist: add NSCameraUsageDescription and NSPhotoLibraryUsageDescription
- recognition_service.dart: RecognitionService wrapping /ai/* endpoints;
  RecognizedItem, ReceiptResult, DishResult models
- scan_screen.dart: mode selector (receipt / products / dish / manual);
  image source picker; loading overlay; navigates to confirm or dish screen
- recognition_confirm_screen.dart: editable list of recognized items;
  inline qty/unit editing; swipe-to-delete; batch-add to pantry
- dish_result_screen.dart: dish name, KBZHU breakdown, similar dishes chips
- app_router.dart: /scan, /scan/confirm, /scan/dish routes (no bottom nav)
- products_screen.dart: FAB now shows bottom sheet with Manual / Scan options

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

client/lib/features/products/products_screen.dart

@@ -5,6 +5,35 @@ import 'package:go_router/go_router.dart';
 import '../../shared/models/product.dart';
 import 'product_provider.dart';
 
+void _showAddMenu(BuildContext context) {
+  showModalBottomSheet(
+    context: context,
+    builder: (_) => SafeArea(
+      child: Column(
+        mainAxisSize: MainAxisSize.min,
+        children: [
+          ListTile(
+            leading: const Icon(Icons.edit_outlined),
+            title: const Text('Добавить вручную'),
+            onTap: () {
+              Navigator.pop(context);
+              context.push('/products/add');
+            },
+          ),
+          ListTile(
+            leading: const Icon(Icons.document_scanner_outlined),
+            title: const Text('Сканировать чек или фото'),
+            onTap: () {
+              Navigator.pop(context);
+              context.push('/scan');
+            },
+          ),
+        ],
+      ),
+    ),
+  );
+}
+
 class ProductsScreen extends ConsumerWidget {
   const ProductsScreen({super.key});
 
@@ -23,7 +52,7 @@ class ProductsScreen extends ConsumerWidget {
         ],
       ),
       floatingActionButton: FloatingActionButton.extended(
-        onPressed: () => context.push('/products/add'),
+        onPressed: () => _showAddMenu(context),
         icon: const Icon(Icons.add),
         label: const Text('Добавить'),
       ),
@@ -34,7 +63,7 @@ class ProductsScreen extends ConsumerWidget {
         ),
         data: (products) => products.isEmpty
             ? _EmptyState(
-                onAdd: () => context.push('/products/add'),
+                onAdd: () => _showAddMenu(context),
               )
             : _ProductList(products: products),
       ),