feat(遊戲化): 新增大廳、附身、時間流、後日談進度等遊戲化系統功能

新增角色大廳（lobby）邀約與通話、附身（possession）、時鐘（clock）抽象、
時間流與睡眠負債、後日談進度、行為選擇與旁觀反應等模組，並補齊對應冒煙
測試（R~V）與單元測試；同步調整 web/mobile 對應頁面與元件。

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

apps/api/src/clock/clock.module.ts

@@ -0,0 +1,9 @@
+import { Module } from "@nestjs/common";
+import { CLOCK } from "./clock.js";
+import { SystemClockService } from "./system-clock.service.js";
+
+@Module({
+  providers: [SystemClockService, { provide: CLOCK, useExisting: SystemClockService }],
+  exports: [CLOCK, SystemClockService],
+})
+export class ClockModule {}

apps/api/src/clock/clock.ts

@@ -0,0 +1,7 @@
+// T36：可注入時鐘介面。本計畫所有新程式一律從時鐘取時間、不直接 `new Date()`，
+// 以便測試以 ControllableClock（見 controllable-clock.ts）快轉時間而不需真的等待。
+export interface Clock {
+  now(): Date;
+}
+
+export const CLOCK = Symbol("CLOCK");

apps/api/src/clock/controllable-clock.test.ts

@@ -0,0 +1,22 @@
+import { describe, expect, it } from "vitest";
+import { ControllableClock } from "./controllable-clock.js";
+
+describe("ControllableClock", () => {
+  it("回報設定時刻，不隨真實時間流動", () => {
+    const clock = new ControllableClock("2026-08-18T00:00:00.000Z");
+    expect(clock.now().toISOString()).toBe("2026-08-18T00:00:00.000Z");
+    expect(clock.now().toISOString()).toBe("2026-08-18T00:00:00.000Z");
+  });
+
+  it("可快轉跨夜情境，秒級內完成", () => {
+    const clock = new ControllableClock("2026-08-18T23:50:00.000Z");
+    clock.advance(20 * 60 * 1000); // 快轉 20 分鐘跨過午夜
+    expect(clock.now().toISOString()).toBe("2026-08-19T00:10:00.000Z");
+  });
+
+  it("set() 可直接指定新時刻", () => {
+    const clock = new ControllableClock();
+    clock.set("2026-01-01T00:00:00.000Z");
+    expect(clock.now().toISOString()).toBe("2026-01-01T00:00:00.000Z");
+  });
+});

apps/api/src/clock/controllable-clock.ts

@@ -0,0 +1,23 @@
+import type { Clock } from "./clock.js";
+
+// T36 測試專用時鐘：可任意設定與快轉當前時間，讓「跨夜→角色去睡→房間關閉」這類情境
+// 在秒級內於測試中重現，不需真的等待。正式環境一律使用 SystemClockService。
+export class ControllableClock implements Clock {
+  private current: Date;
+
+  constructor(initial: Date | string | number = new Date(0)) {
+    this.current = new Date(initial);
+  }
+
+  now(): Date {
+    return this.current;
+  }
+
+  set(date: Date | string | number): void {
+    this.current = new Date(date);
+  }
+
+  advance(ms: number): void {
+    this.current = new Date(this.current.getTime() + ms);
+  }
+}

apps/api/src/clock/system-clock.service.ts

@@ -0,0 +1,9 @@
+import { Injectable } from "@nestjs/common";
+import type { Clock } from "./clock.js";
+
+@Injectable()
+export class SystemClockService implements Clock {
+  now(): Date {
+    return new Date();
+  }
+}