fix(gateway): 일시정지와 서버 중지 상태 계약 분리

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

@@ -1,3 +1,4 @@
+import { gatewayProfileCapabilities, type GatewayProfileStatus } from '@sammo-ts/common';
 import { createGatewayPostgresConnector } from '@sammo-ts/infra';
 
 export interface GatewayProfileGateOptions {
@@ -15,8 +16,6 @@ export interface GatewayProfileGate {
 
 const DEFAULT_CACHE_MS = 2000;
 
-const isRunningStatus = (status: string | null | undefined): boolean => status === 'RUNNING';
-
 export const createGatewayProfileGate = async (options: GatewayProfileGateOptions): Promise<GatewayProfileGate> => {
     const connector = createGatewayPostgresConnector({
         url: options.gatewayDatabaseUrl ?? options.databaseUrl,
@@ -34,7 +33,7 @@ export const createGatewayProfileGate = async (options: GatewayProfileGateOption
             if (!profile) {
                 return false;
             }
-            return !isRunningStatus(profile.status);
+            return !gatewayProfileCapabilities(profile.status as GatewayProfileStatus).turnsRunning;
         } catch {
             return false;
         }