userfront&backend test coverage 추가

userfront/test/login_link_route_policy_test.dart

@@ -29,5 +29,47 @@ void main() {
       );
       expect(isPublic, isTrue);
     });
+
+    test('public auth path 목록을 허용하고 일반 보호 경로는 제외한다', () {
+      final publicPaths = [
+        '/signin',
+        '/signup',
+        '/login',
+        '/registration',
+        '/verify',
+        '/verification',
+        '/verify-complete',
+        '/verify/token',
+        '/l/AB123456',
+        '/approve',
+        '/ql/AB123456',
+        '/forgot-password',
+        '/recovery',
+        '/reset-password',
+        '/error',
+        '/settings',
+        '/consent',
+        '/consent/challenge',
+      ];
+
+      for (final path in publicPaths) {
+        expect(isPublicAuthPath(path, Uri.parse(path)), isTrue, reason: path);
+      }
+
+      expect(
+        isPublicAuthPath('/dashboard', Uri.parse('/ko/dashboard')),
+        isFalse,
+      );
+      expect(
+        isPublicAuthPath('/dashboard', Uri.parse('/ko/auth/consent/callback')),
+        isTrue,
+      );
+    });
+
+    test('short code route가 아니면 null을 반환한다', () {
+      expect(extractLoginShortCode(Uri.parse('/login')), isNull);
+      expect(extractLoginShortCode(Uri.parse('/l')), isNull);
+      expect(extractLoginShortCode(Uri.parse('/x/AB123456')), isNull);
+    });
   });
 }