refactor: v2 重构 — 模块化拆分 + AI Prompt模板化 + 前端状态管理

P0 - AI交互层:
- ai/prompt.js: 模块化 Prompt 模板
- ai/validator.js: JSON Schema 校验 + normalize
- ai/client.js: DeepSeek API 封装
- 金额计算唯一化，时间格式归一化

P1 - 后端架构:
- routes/: auth/rooms/messages/purchases 独立路由
- middleware/auth.js: 认证授权中间件
- ws/index.js: WebSocket 连接管理
- db.js: 启用 foreign_keys
- server.js: 从588行精简到40行入口

P2 - 前端架构:
- public/css/style.css: CSS 独立
- public/js/store.js: 全局状态 Store
- public/js/{chat,ws,purchases,auth}.js: 功能模块拆分
- index.html: 纯 HTML 结构, v2.6

server/public/js/auth.js

@@ -0,0 +1,54 @@
+// 认证与初始化
+async function init() {
+  const token = Store.getToken();
+  if (token) {
+    try {
+      const res = await fetch('/api/user', { headers: { 'Authorization': `Bearer ${token}` } });
+      if (res.ok) {
+        const user = await res.json();
+        document.getElementById('login-page').classList.add('hidden');
+        document.getElementById('main-page').classList.remove('hidden');
+        if (localStorage.getItem('isAdmin') === 'true') {
+          document.getElementById('create-room-btn').classList.add('visible');
+        } else {
+          document.getElementById('create-room-btn').classList.remove('visible');
+        }
+        initWebSocket();
+        loadRooms();
+        updateSummaryPreview();
+        initSwipeGestures();
+        return;
+      }
+    } catch(e) {}
+    Store.clearAuth();
+  }
+  document.getElementById('login-page').classList.remove('hidden');
+  document.getElementById('main-page').classList.add('hidden');
+}
+
+async function login() {
+  const u = document.getElementById('login-user').value;
+  const p = document.getElementById('login-pass').value;
+  const res = await fetch('/api/login', {
+    method: 'POST', headers: { 'Content-Type': 'application/json' },
+    body: JSON.stringify({ username: u, password: p })
+  });
+  if (res.ok) {
+    const data = await res.json();
+    Store.saveAuth(data);
+    document.getElementById('login-page').classList.add('hidden');
+    document.getElementById('main-page').classList.remove('hidden');
+    if (data.isAdmin) {
+      document.getElementById('create-room-btn').classList.add('visible');
+    } else {
+      document.getElementById('create-room-btn').classList.remove('visible');
+    }
+    initWebSocket();
+    loadRooms();
+    updateSummaryPreview();
+    initSwipeGestures();
+  } else {
+    const err = await res.json();
+    document.getElementById('login-error').textContent = err.error || '登录失败';
+  }
+}