feat: 首页添加用户登录状态指示器

- 已登录：右上角显示头像 + 用户名，点击进入个人中心
- 未登录：右上角显示"登录"按钮，点击弹出注册/登录弹窗

src/app/page.tsx

@@ -1,12 +1,27 @@
 "use client";
 
+import { useState, useEffect, useCallback } from "react";
 import { useRouter } from "next/navigation";
 import { motion } from "framer-motion";
-import { Zap, Gift, Clock, ChevronRight } from "lucide-react";
+import { Zap, Gift, Clock, ChevronRight, User } from "lucide-react";
 import BrandLogo from "@/components/BrandLogo";
+import { getCachedProfile } from "@/lib/userId";
+import AuthModal from "@/components/AuthModal";
+import type { UserProfile } from "@/types";
 
 export default function LandingPage() {
   const router = useRouter();
+  const [profile, setProfile] = useState<UserProfile | null>(null);
+  const [showAuth, setShowAuth] = useState(false);
+
+  useEffect(() => {
+    setProfile(getCachedProfile());
+  }, []);
+
+  const handleAuth = useCallback((p: UserProfile) => {
+    setProfile(p);
+    setShowAuth(false);
+  }, []);
 
   return (
     <div className="relative flex min-h-dvh flex-col items-center bg-background px-5 py-10 overflow-y-auto scrollbar-none">
@@ -14,6 +29,32 @@ export default function LandingPage() {
       <div className="pointer-events-none fixed left-1/2 top-0 -translate-x-1/2 -translate-y-1/3 h-[420px] w-[420px] rounded-full bg-orange-500/8 blur-3xl" />
       <div className="pointer-events-none fixed left-1/4 top-1/2 h-[300px] w-[300px] rounded-full bg-purple-500/5 blur-3xl" />
 
+      {/* User indicator */}
+      <motion.div
+        className="mb-4 flex w-full max-w-sm justify-end"
+        initial={{ opacity: 0 }}
+        animate={{ opacity: 1 }}
+        transition={{ delay: 0.1 }}
+      >
+        {profile ? (
+          <button
+            onClick={() => router.push("/profile")}
+            className="flex items-center gap-2 rounded-full bg-surface/80 px-3 py-1.5 ring-1 ring-border/50 backdrop-blur-sm transition-colors hover:bg-elevated"
+          >
+            <span className="text-sm">{profile.avatar}</span>
+            <span className="text-xs font-semibold text-gray-300">{profile.username}</span>
+          </button>
+        ) : (
+          <button
+            onClick={() => setShowAuth(true)}
+            className="flex items-center gap-1.5 rounded-full bg-surface/80 px-3 py-1.5 text-xs font-medium text-muted ring-1 ring-border/50 backdrop-blur-sm transition-colors hover:bg-elevated hover:text-gray-300"
+          >
+            <User size={13} />
+            登录
+          </button>
+        )}
+      </motion.div>
+
       {/* Header */}
       <motion.div
         className="flex flex-col items-center gap-4"
@@ -147,6 +188,13 @@ export default function LandingPage() {
       >
         NOWHATEVER — 拒绝随便，从今天开始
       </motion.p>
+
+      <AuthModal
+        open={showAuth}
+        onClose={() => setShowAuth(false)}
+        onAuth={handleAuth}
+        defaultTab="register"
+      />
     </div>
   );
 }