refactor: UI 화면 통합 및 불필요한 파일 정리

- 모든 *_redesign.dart 파일을 기본 화면 파일로 통합
- 백업용 컨트롤러 파일들 제거 (*_controller.backup.dart)
- 사용하지 않는 예제 및 테스트 파일 제거
- Clean Architecture 적용 후 남은 정리 작업 완료
- 테스트 코드 정리 및 구조 개선 준비

🤖 Generated with [Claude Code](https://claude.ai/code)

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

lib/domain/usecases/equipment/equipment_in_usecase.dart

@@ -1,6 +1,5 @@
 import 'package:dartz/dartz.dart';
 import '../../../services/equipment_service.dart';
-import '../../../data/models/equipment/equipment_in_request.dart';
 import '../../../data/models/equipment/equipment_io_response.dart';
 import '../../../core/errors/failures.dart';
 import '../base_usecase.dart';

lib/domain/usecases/equipment/equipment_out_usecase.dart

@@ -1,6 +1,5 @@
 import 'package:dartz/dartz.dart';
 import '../../../services/equipment_service.dart';
-import '../../../data/models/equipment/equipment_out_request.dart';
 import '../../../data/models/equipment/equipment_io_response.dart';
 import '../../../core/errors/failures.dart';
 import '../base_usecase.dart';

lib/domain/usecases/equipment/get_equipments_usecase.dart

@@ -2,6 +2,7 @@ import 'package:dartz/dartz.dart';
 import '../../../services/equipment_service.dart';
 import '../../../models/equipment_unified_model.dart';
 import '../../../core/errors/failures.dart';
+import '../../../data/models/common/paginated_response.dart';
 import '../base_usecase.dart';
 
 /// 장비 목록 조회 파라미터
@@ -25,13 +26,13 @@ class GetEquipmentsParams {
 
 /// 장비 목록 조회 UseCase
 /// 필터링 및 페이지네이션 지원
-class GetEquipmentsUseCase extends UseCase<List<Equipment>, GetEquipmentsParams> {
+class GetEquipmentsUseCase extends UseCase<PaginatedResponse<Equipment>, GetEquipmentsParams> {
   final EquipmentService _equipmentService;
 
   GetEquipmentsUseCase(this._equipmentService);
 
   @override
-  Future<Either<Failure, List<Equipment>>> call(GetEquipmentsParams params) async {
+  Future<Either<Failure, PaginatedResponse<Equipment>>> call(GetEquipmentsParams params) async {
     try {
       // 상태 유효성 검증
       if (params.status != null &&