feat(app): finalize ad gated flows and weather

- add AppLogger and replace scattered print logging\n- implement ad-gated recommendation flow with reminder handling and calendar link\n- complete Bluetooth share pipeline with ad gate and merge\n- integrate KMA weather API with caching and dart-define decoding\n- add NaverUrlProcessor refactor and restore restaurant repository tests

lib/data/api/naver/naver_proxy_client.dart

@@ -1,5 +1,6 @@
 import 'package:dio/dio.dart';
 import 'package:flutter/foundation.dart';
+import 'package:lunchpick/core/utils/app_logger.dart';
 
 import '../../../core/network/network_client.dart';
 import '../../../core/network/network_config.dart';
@@ -22,7 +23,7 @@ class NaverProxyClient {
 
     try {
       final proxyUrl = NetworkConfig.getCorsProxyUrl(url);
-      debugPrint('Using proxy URL: $proxyUrl');
+      AppLogger.debug('Using proxy URL: $proxyUrl');
 
       final response = await _networkClient.get<String>(
         proxyUrl,
@@ -42,9 +43,13 @@ class NaverProxyClient {
 
       return response.data!;
     } on DioException catch (e) {
-      debugPrint('Proxy fetch error: ${e.message}');
-      debugPrint('Status code: ${e.response?.statusCode}');
-      debugPrint('Response: ${e.response?.data}');
+      AppLogger.error(
+        'Proxy fetch error: ${e.message}',
+        error: e,
+        stackTrace: e.stackTrace,
+      );
+      AppLogger.debug('Status code: ${e.response?.statusCode}');
+      AppLogger.debug('Response: ${e.response?.data}');
 
       if (e.response?.statusCode == 403) {
         throw ServerException(
@@ -78,8 +83,12 @@ class NaverProxyClient {
       );
 
       return response.statusCode == 200;
-    } catch (e) {
-      debugPrint('Proxy status check failed: $e');
+    } catch (e, stackTrace) {
+      AppLogger.error(
+        'Proxy status check failed: $e',
+        error: e,
+        stackTrace: stackTrace,
+      );
       return false;
     }
   }