feat: Add Request functionality to All Cars tab

- Add checkbox selection for cars in All Cars tab when requestId is present
- Add "Add to Request" button with selection count
- Add select all/deselect all functionality
- Highlight selected cars with blue ring

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

frontend/src/app/admin/cars/page.tsx

@@ -151,6 +151,8 @@ export default function CarsAdminPage() {
   const [allCarsLoading, setAllCarsLoading] = useState(false);
   const [allCarsTotal, setAllCarsTotal] = useState(0);
   const [allCarsPage, setAllCarsPage] = useState(1);
+  const [selectedAllCars, setSelectedAllCars] = useState<Set<number>>(new Set());
+  const [addingAllCarsToRequest, setAddingAllCarsToRequest] = useState(false);
 
   // Carmodoo search state
   const [makers, setMakers] = useState<CarmodooMaker[]>([]);
@@ -1093,6 +1095,92 @@ export default function CarsAdminPage() {
     }
   };
 
+  // All Cars 탭에서 Request에 추가하는 함수
+  const handleAddAllCarsToRequest = async () => {
+    if (!requestId) return;
+    if (selectedAllCars.size === 0) {
+      alert('Please select at least one car to add to the request.');
+      return;
+    }
+
+    if (!confirm(`${selectedAllCars.size}개의 차량을 추천 목록에 추가하시겠습니까?`)) {
+      return;
+    }
+
+    setAddingAllCarsToRequest(true);
+
+    try {
+      const selectedCarsList = allCars.filter(car => selectedAllCars.has(car.id));
+      let addedCount = 0;
+      let errorCount = 0;
+
+      for (const car of selectedCarsList) {
+        try {
+          const mainImage = car.images?.find((img) => img.is_main)?.url || car.images?.[0]?.url;
+          await vehicleRequestsApi.adminAddVehicle(parseInt(requestId), {
+            request_id: parseInt(requestId),
+            car_id: car.id,  // 이미 로컬 DB에 있는 차량이므로 car_id 사용
+            car_data: {
+              id: car.id.toString(),
+              car_name: car.car_name,
+              maker_name: car.maker?.name,
+              model_name: car.model?.name,
+              year: car.year,
+              mileage: car.mileage,
+              final_price: car.final_price_krw || car.price_krw,
+              fuel: car.fuel,
+              transmission: car.transmission,
+              color: car.color,
+              main_image: mainImage,
+            },
+            is_approved: true,
+          });
+          addedCount++;
+        } catch (err) {
+          console.error(`Failed to add car ${car.id}:`, err);
+          errorCount++;
+        }
+      }
+
+      setSelectedAllCars(new Set());
+
+      if (errorCount > 0) {
+        alert(`${addedCount}개의 차량이 추천 목록에 추가되었습니다.\n(실패: ${errorCount}개)`);
+      } else {
+        alert(`${addedCount}개의 차량이 추천 목록에 추가되었습니다.`);
+      }
+
+      router.push('/admin/vehicle-requests');
+    } catch (err) {
+      console.error('Add to request failed:', err);
+      alert('추천 목록 추가에 실패했습니다.');
+    } finally {
+      setAddingAllCarsToRequest(false);
+    }
+  };
+
+  // All Cars 선택 토글
+  const toggleAllCarSelection = (carId: number) => {
+    setSelectedAllCars(prev => {
+      const newSet = new Set(prev);
+      if (newSet.has(carId)) {
+        newSet.delete(carId);
+      } else {
+        newSet.add(carId);
+      }
+      return newSet;
+    });
+  };
+
+  // All Cars 전체 선택/해제
+  const handleSelectAllAllCars = () => {
+    if (selectedAllCars.size === allCars.length) {
+      setSelectedAllCars(new Set());
+    } else {
+      setSelectedAllCars(new Set(allCars.map(car => car.id)));
+    }
+  };
+
   const handleDeleteCar = async (carId: number) => {
     if (!confirm('Are you sure you want to delete this car?')) {
       return;
@@ -1700,6 +1788,45 @@ export default function CarsAdminPage() {
             This shows the cars that are visible to users (is_displayed = true). This is the same view as the public /cars page.
           </p>
 
+          {/* Selection Controls for Request Mode */}
+          {requestId && allCars.length > 0 && (
+            <div className="flex items-center justify-between mb-4 p-3 bg-blue-50 rounded-lg">
+              <div className="flex items-center gap-4">
+                <label className="flex items-center gap-2 cursor-pointer">
+                  <input
+                    type="checkbox"
+                    checked={selectedAllCars.size === allCars.length && allCars.length > 0}
+                    onChange={handleSelectAllAllCars}
+                    className="w-5 h-5 text-primary-600 rounded"
+                  />
+                  <span className="text-sm font-medium text-gray-700">Select All</span>
+                </label>
+                <span className="text-sm text-blue-600 font-medium">
+                  {selectedAllCars.size} selected
+                </span>
+              </div>
+              <button
+                onClick={handleAddAllCarsToRequest}
+                disabled={addingAllCarsToRequest || selectedAllCars.size === 0}
+                className="bg-blue-600 text-white px-4 py-2 rounded-lg hover:bg-blue-700 transition-colors disabled:opacity-50 flex items-center gap-2"
+              >
+                {addingAllCarsToRequest ? (
+                  <>
+                    <div className="w-4 h-4 border-2 border-white border-t-transparent rounded-full animate-spin"></div>
+                    <span>Adding...</span>
+                  </>
+                ) : (
+                  <>
+                    <svg className="w-5 h-5" fill="none" stroke="currentColor" viewBox="0 0 24 24">
+                      <path strokeLinecap="round" strokeLinejoin="round" strokeWidth={2} d="M12 6v6m0 0v6m0-6h6m-6 0H6" />
+                    </svg>
+                    <span>Add to Request #{requestId}</span>
+                  </>
+                )}
+              </button>
+            </div>
+          )}
+
           {allCarsLoading ? (
             <div className="flex justify-center py-12">
               <div className="w-8 h-8 border-4 border-primary-600 border-t-transparent rounded-full animate-spin"></div>
@@ -1717,13 +1844,30 @@ export default function CarsAdminPage() {
               <div className="grid grid-cols-1 sm:grid-cols-2 lg:grid-cols-3 xl:grid-cols-4 gap-4">
                 {allCars.map((car) => {
                   const mainImage = getImageUrl(car.images?.find((img) => img.is_main)?.url || car.images?.[0]?.url);
+                  const isSelected = selectedAllCars.has(car.id);
                   return (
                     <div
                       key={car.id}
-                      className="border rounded-lg overflow-hidden hover:shadow-md transition cursor-pointer"
+                      className={`border rounded-lg overflow-hidden hover:shadow-md transition cursor-pointer ${
+                        isSelected ? 'ring-2 ring-blue-500 border-blue-500' : ''
+                      }`}
                       onClick={() => handleCarClick(car)}
                     >
                       <div className="relative h-40 bg-gray-100">
+                        {/* Checkbox for Request Mode */}
+                        {requestId && (
+                          <div
+                            className="absolute top-2 left-2 z-10"
+                            onClick={(e) => e.stopPropagation()}
+                          >
+                            <input
+                              type="checkbox"
+                              checked={isSelected}
+                              onChange={() => toggleAllCarSelection(car.id)}
+                              className="w-5 h-5 text-blue-600 rounded cursor-pointer"
+                            />
+                          </div>
+                        )}
                         {mainImage ? (
                           <img
                             src={mainImage}