fix(engine): 서버 재개 시 게임 시계를 Ref 기준으로 보정한다

짧은 중단은 순서대로 따라잡고 장기 중단은 턴 간격별 Ref 한도를 넘어선 완전 턴을 일괄 이동한다. 장수와 미완료 경매 시각을 같은 트랜잭션에서 저장하고 표시 시각 지연을 복구한다.

app/game-engine/src/turn/databaseHooks.ts

@@ -379,7 +379,7 @@ export const summarizeRealtimeReadModelChanges = (
         lobbyGeneralIds,
         reservedGeneralIds,
         recordGeneralIds,
-        worldChanged: false,
+        worldChanged: changes.realtimeBacklogShiftTicks > 0,
         globalRecordsChanged,
         worldHistoryChanged,
         contactsChanged,
@@ -1078,6 +1078,7 @@ export const createDatabaseTurnHooks = async (
         let persistedVisibleLogs: PersistedVisibleLogRow[] = [];
         let visibleLogFloor = directLogFloor;
         const {
+            realtimeBacklogShiftTicks,
             accessScoreResetGeneralIds,
             generals,
             cities,
@@ -1161,6 +1162,27 @@ export const createDatabaseTurnHooks = async (
                 data: worldStateUpdate,
             });
 
+            if (realtimeBacklogShiftTicks > 0) {
+                const deltaTicks = BigInt(realtimeBacklogShiftTicks);
+                const deltaSeconds = (realtimeBacklogShiftTicks / GAME_TICKS_PER_TURN) * state.tickSeconds;
+                await prisma.$executeRaw(
+                    GamePrisma.sql`
+                        UPDATE general
+                        SET turn_tick = CASE WHEN turn_tick IS NULL THEN NULL ELSE turn_tick + ${deltaTicks} END,
+                            turn_time = turn_time + (${deltaSeconds} * INTERVAL '1 second')
+                    `
+                );
+                await prisma.$executeRaw(
+                    GamePrisma.sql`
+                        UPDATE auction
+                        SET close_tick = CASE WHEN close_tick IS NULL THEN NULL ELSE close_tick + ${deltaTicks} END,
+                            close_at = close_at + (${deltaSeconds} * INTERVAL '1 second'),
+                            updated_at = NOW()
+                        WHERE status = 'OPEN'
+                    `
+                );
+            }
+
             if (
                 state.tickSeconds !== persistedTickSeconds &&
                 commandCompletion?.result.type !== 'updateRuntimeSettings'