feat: 응답 가능한 서신과 턴 시간 호환 이관

등용장과 이민족 선택 응답을 turn daemon transaction으로 연결하고 Ref의 통일 이후 상태 전이와 수신자별 메시지 저장 규칙을 보존한다.\n\n유산 턴 시간 변경을 nextTurnTimeBase 기반 결정적 계산으로 바로잡고 API, 엔진, Chromium 회귀를 추가한다.

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

@@ -0,0 +1,36 @@
+import { describe, expect, it } from 'vitest';
+
+import { resolveResetTurnTimeBase } from '../src/router/inherit/index.js';
+
+describe('inherit reset turn time Ref compatibility', () => {
+    it('matches the Ref PHP deterministic seed, offset, and displayed minute', () => {
+        const result = resolveResetTurnTimeBase({
+            hiddenSeed: 'hidden-seed',
+            userId: 'user-7',
+            previousTurnTimeBase: 123_456,
+            tickSeconds: 600,
+        });
+
+        expect(result.nextTurnTimeBase).toBeCloseTo(302.5143852464758, 12);
+        expect(result.nextTurnTimeLabel).toBe('00:05');
+    });
+
+    it('uses the prior pending base as the next deterministic seed input', () => {
+        const first = resolveResetTurnTimeBase({
+            hiddenSeed: 'hidden-seed',
+            userId: 'user-7',
+            previousTurnTimeBase: 123_456,
+            tickSeconds: 600,
+        });
+        const second = resolveResetTurnTimeBase({
+            hiddenSeed: 'hidden-seed',
+            userId: 'user-7',
+            previousTurnTimeBase: first.nextTurnTimeBase,
+            tickSeconds: 600,
+        });
+
+        expect(second.nextTurnTimeBase).not.toBe(first.nextTurnTimeBase);
+        expect(second.nextTurnTimeBase).toBeGreaterThanOrEqual(0);
+        expect(second.nextTurnTimeBase).toBeLessThan(600);
+    });
+});