fix: correct dashboard freshness wiring

backend/src/dashboard/dashboard.service.ts

@@ -218,15 +218,18 @@ export class DashboardService {
     const freshness: FreshnessMeta = {
       generatedAt: new Date().toISOString(),
       activityLatestAt: activities[0]?.createdAt?.toISOString() ?? null,
-      sistersLatestAt: sisters
-        .map((sister) => sister.lastSeen)
-        .filter((value): value is Date => value instanceof Date)
-        .sort((a, b) => b.getTime() - a.getTime())[0]
-        ?.toISOString() ?? null,
-      qaDocLatestAt: board
-        .filter((item) => item.category === 'qa-log')
-        .map((item) => item.time)
-        .sort((a, b) => new Date(b).getTime() - new Date(a).getTime())[0] ?? null,
+      sistersLatestAt:
+        sisters
+          .map((sister) => sister.lastSeen)
+          .filter((value): value is Date => value instanceof Date)
+          .sort((a, b) => b.getTime() - a.getTime())[0]
+          ?.toISOString() ?? null,
+      qaDocLatestAt:
+        board
+          .filter((item) => item.category === 'DOC-DERIVED')
+          .map((item) => item.time)
+          .sort((a, b) => new Date(b).getTime() - new Date(a).getTime())[0] ??
+        null,
     };
 
     return {

frontend/app/page.tsx

@@ -1197,7 +1197,7 @@ export default function DashboardPage() {
               <InfraCard key={card.title}>
                 <InfraTitle>{card.title}</InfraTitle>
                 <InfraMeta>{card.meta}</InfraMeta>
-                <EventTag $tone={card.title === 'Gateway / Runtime' && connected ? 'ok' : card.detail.includes('없음') ? 'default' : 'active'}>{card.detail}</EventTag>
+                <EventTag $tone={card.title === 'Runtime' && connected ? 'ok' : card.detail.startsWith('NO ') ? 'default' : 'active'}>{card.detail}</EventTag>
               </InfraCard>
             ))}
           </InfraMap>