fix: [생산지시] 날짜포맷·개소수·자재투입 시 자동 상태전환

- ProductionOrderService: production_ordered_at를 Y-m-d 포맷으로 변환
- ProductionOrderService: withCount('nodes')로 개소수(node_count) 응답 추가
- WorkOrderService: autoStartWorkOrderOnMaterialInput() 신규 메서드
  - 자재투입 시 WO가 unassigned/pending/waiting이면 in_progress로 자동 전환
  - syncOrderStatus()로 Order도 IN_PRODUCTION 동기화
- Swagger: node_count 필드 문서화, 날짜 포맷 수정

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

app/Services/ProductionOrderService.php

@@ -29,7 +29,7 @@ public function index(array $params): LengthAwarePaginator
             ->where('tenant_id', $tenantId)
             ->whereIn('status_code', self::PRODUCTION_STATUSES)
             ->with(['client', 'workOrders.process', 'workOrders.assignees.user'])
-            ->withCount('workOrders');
+            ->withCount(['workOrders', 'nodes']);
 
         // 검색어 필터
         if (! empty($params['search'])) {
@@ -71,7 +71,13 @@ public function index(array $params): LengthAwarePaginator
 
         // 가공 필드 추가
         $result->getCollection()->transform(function (Order $order) {
-            $order->production_ordered_at = $order->workOrders->min('created_at');
+            $minCreatedAt = $order->workOrders->min('created_at');
+            $order->production_ordered_at = $minCreatedAt
+                ? $minCreatedAt->format('Y-m-d')
+                : null;
+
+            // 개소수 (order_nodes 수)
+            $order->node_count = $order->nodes_count ?? 0;
 
             $workOrders = $order->workOrders;
             $order->work_order_progress = [
@@ -138,10 +144,14 @@ public function show(int $orderId): array
                 'workOrders.assignees.user',
                 'nodes',
             ])
+            ->withCount('nodes')
             ->findOrFail($orderId);
 
-        // 생산지시일
-        $order->production_ordered_at = $order->workOrders->min('created_at');
+        // 생산지시일 (날짜만)
+        $minCreatedAt = $order->workOrders->min('created_at');
+        $order->production_ordered_at = $minCreatedAt
+            ? $minCreatedAt->format('Y-m-d')
+            : null;
         $order->production_status = $this->mapProductionStatus($order->status_code);
 
         // WorkOrder 진행 현황
@@ -171,6 +181,7 @@ public function show(int $orderId): array
             'order' => $order->makeHidden(['workOrders', 'nodes']),
             'production_ordered_at' => $order->production_ordered_at,
             'production_status' => $order->production_status,
+            'node_count' => $order->nodes_count ?? 0,
             'work_order_progress' => $workOrderProgress,
             'work_orders' => $workOrders,
             'bom_process_groups' => $bomProcessGroups,