feat: 用户名密码登录注册系统

- 新增 /api/auth/register 和 /api/auth/login 接口，使用 bcryptjs 哈希密码
- User 模型改为 username + passwordHash，id 自动生成 cuid
- 新增 AuthModal 组件（登录/注册双标签页），替换旧的 ProfileSetupModal
- 重写 /profile 页面：支持修改用户名、密码、头像、绑定邮箱、退出登录
- /api/user PUT 支持密码修改（需验证当前密码）和用户名唯一性校验
- 游客模式保留，右上角显示"登录"按钮；登录后显示头像和用户名
- 全局 nickname -> username 重命名（types、SwipeDeck、RoomManageModal、buildRoomStatus）
- 新增 logout() 清除登录态并重新生成游客 UUID

src/app/page.tsx

@@ -3,8 +3,11 @@
 import { useState, useRef, useEffect, useCallback } from "react";
 import { useRouter } from "next/navigation";
 import { motion, AnimatePresence } from "framer-motion";
-import { Plus, LogIn, Utensils, Loader2, MapPin, Navigation, X, Users, Heart, Sparkles, ChevronRight, Flame } from "lucide-react";
-import { getUserId } from "@/lib/userId";
+import { Plus, LogIn, Loader2, MapPin, Navigation, X, Users, Heart, Sparkles, ChevronRight, Flame, User } from "lucide-react";
+import { getUserId, getCachedProfile, getCachedPreferences } from "@/lib/userId";
+import { getAvatarBg } from "@/lib/avatars";
+import AuthModal from "@/components/AuthModal";
+import type { UserProfile } from "@/types";
 
 interface LocationSuggestion {
   id: string;
@@ -70,6 +73,19 @@ export default function LandingPage() {
   const suggestRef = useRef<HTMLDivElement>(null);
   const debounceRef = useRef<ReturnType<typeof setTimeout>>(null);
 
+  const [profile, setProfile] = useState<UserProfile | null>(null);
+  const [authModalOpen, setAuthModalOpen] = useState(false);
+
+  useEffect(() => {
+    const cached = getCachedProfile();
+    if (cached) setProfile(cached);
+
+    const prefs = getCachedPreferences();
+    if (prefs.cuisine) setCuisine(prefs.cuisine);
+    if (prefs.priceRange) setPriceRange(prefs.priceRange);
+    if (prefs.radius) setRadius(prefs.radius);
+  }, []);
+
   const fetchSuggestions = useCallback(async (query: string) => {
     if (query.length < 1) {
       setSuggestions([]);
@@ -191,7 +207,28 @@ export default function LandingPage() {
   };
 
   return (
-    <div className="flex min-h-dvh flex-col items-center justify-center bg-background px-6 py-12">
+    <div className="relative flex min-h-dvh flex-col items-center justify-center bg-background px-6 py-12">
+      {/* Profile / Auth button */}
+      <div className="absolute right-4 top-4">
+        {profile ? (
+          <button
+            onClick={() => router.push("/profile")}
+            className={`flex h-9 items-center gap-1.5 rounded-full px-3 text-sm font-medium transition-colors active:opacity-80 ${getAvatarBg(profile.avatar)}`}
+          >
+            <span className="text-base leading-none">{profile.avatar}</span>
+            <span className="max-w-[5rem] truncate text-xs font-semibold text-zinc-700">{profile.username}</span>
+          </button>
+        ) : (
+          <button
+            onClick={() => setAuthModalOpen(true)}
+            className="flex h-9 items-center gap-1.5 rounded-full bg-zinc-100 px-3 text-xs font-medium text-zinc-500 transition-colors active:bg-zinc-200"
+          >
+            <User size={14} />
+            登录
+          </button>
+        )}
+      </div>
+
       <motion.div
         className="flex flex-col items-center"
         initial={{ y: -20, opacity: 0 }}
@@ -466,6 +503,12 @@ export default function LandingPage() {
           </motion.p>
         )}
       </motion.div>
+
+      <AuthModal
+        open={authModalOpen}
+        onClose={() => setAuthModalOpen(false)}
+        onAuth={(p) => setProfile(p)}
+      />
     </div>
   );
 }