perf: 전투 시뮬레이터 시작 payload를 줄인다

권위 실행 context를 화면 진입 때 한 번 전달하고 준비 응답은 seed base만 반환한다. 반복별 seed 배열은 결정적 파생값으로 대체하되 구형 queue seed 우선순위와 고정 seed 동작을 보존한다.

app/game-api/test/battleSimProcessor.test.ts

@@ -266,6 +266,7 @@ describe('battle sim processor', () => {
         const firstPayload = buildPayload('battle');
         delete firstPayload.seed;
         firstPayload.repeatCnt = 2;
+        firstPayload.seedBase = 'ignored-while-legacy-seeds-exist';
         firstPayload.seeds = ['server-repeat-0', 'server-repeat-1'];
         const secondPayload = structuredClone(firstPayload);
         const observedSeeds: string[] = [];
@@ -283,6 +284,30 @@ describe('battle sim processor', () => {
         expect(observedSeeds).toEqual(['server-repeat-0', 'server-repeat-1']);
     });
 
+    it('expands one seed base deterministically without a repeated seed array', () => {
+        const firstPayload = buildPayload('battle');
+        delete firstPayload.seed;
+        firstPayload.repeatCnt = 2;
+        firstPayload.seedBase = 'server-root';
+        const secondPayload = structuredClone(firstPayload);
+        const observedSeeds: string[] = [];
+
+        const first = processBattleSimJob(firstPayload, {
+            rngFactory: (seed) => {
+                observedSeeds.push(seed);
+                return new RandUtil(LiteHashDRBG.build(seed));
+            },
+        });
+        const second = processBattleSimJob(secondPayload);
+
+        expect(first).toEqual(second);
+        expect(first.repeatCnt).toBe(2);
+        expect(observedSeeds).toEqual([
+            'str(11,server-root)|str(16,battle-simulator)|int(0)',
+            'str(11,server-root)|str(16,battle-simulator)|int(1)',
+        ]);
+    });
+
     it('returns the fixed defender ID order for reorder action', () => {
         const payload = buildPayload('reorder');
         const result = processBattleSimJob(payload);