feat: Add search/filter bar to admin cars page

- Backend: Add search (car name/plate number), color, year filters to GET /api/cars
- Frontend: Add filter bar with car name/plate, color, year range inputs
- Clear button resets all filters

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

backend/app/api/cars.py

@@ -64,6 +64,8 @@ def get_cars(
     price_max: Optional[int] = None,
     mileage_max: Optional[int] = None,
     fuel: Optional[str] = None,
+    color: Optional[str] = None,
+    search: Optional[str] = None,
     status: Optional[str] = None,
     is_displayed: Optional[bool] = None,
     admin: bool = Query(False, description="Admin mode - show all cars"),
@@ -85,6 +87,14 @@ def get_cars(
     if is_displayed is not None and admin:
         base_query = base_query.filter(Car.is_displayed == is_displayed)
 
+    # 통합 검색 (차량번호, 차량명)
+    if search:
+        search_term = f"%{search}%"
+        base_query = base_query.filter(
+            (Car.car_number.ilike(search_term)) |
+            (Car.car_name.ilike(search_term))
+        )
+
     if maker_id:
         base_query = base_query.filter(Car.maker_id == maker_id)
     if model_id:
@@ -101,6 +111,8 @@ def get_cars(
         base_query = base_query.filter(Car.mileage <= mileage_max)
     if fuel:
         base_query = base_query.filter(Car.fuel == fuel)
+    if color:
+        base_query = base_query.filter(Car.color.ilike(f"%{color}%"))
 
     total = base_query.count()