fix: AuthModal 重开时重置表单 + 邀请页加入失败显示错误

- #13: useEffect 监听 open 变化时重置所有表单状态（用户名、密码、错误等）
- #14: handleJoin catch 中捕获错误消息并渲染到页面

src/app/invite/[id]/page.tsx

@@ -29,6 +29,7 @@ export default function InvitePage() {
   const [userCount, setUserCount] = useState(0);
   const [scene, setScene] = useState<SceneType>("eat");
   const [joining, setJoining] = useState(false);
+  const [joinError, setJoinError] = useState("");
 
   const sceneConfig = getSceneConfig(scene);
 
@@ -48,10 +49,12 @@ export default function InvitePage() {
 
   const handleJoin = async () => {
     setJoining(true);
+    setJoinError("");
     try {
       await joinRoom(roomId, getUserId());
       router.push(`/room/${roomId}`);
-    } catch {
+    } catch (e) {
+      setJoinError(e instanceof Error ? e.message : "加入失败，请重试");
       setJoining(false);
     }
   };
@@ -187,6 +190,15 @@ export default function InvitePage() {
         animate={{ y: 0, opacity: 1 }}
         transition={{ duration: 0.5, delay: 0.3 }}
       >
+        {joinError && (
+          <motion.p
+            className="mb-3 text-center text-xs font-medium text-rose-400"
+            initial={{ opacity: 0, y: -4 }}
+            animate={{ opacity: 1, y: 0 }}
+          >
+            {joinError}
+          </motion.p>
+        )}
         <Button
           onClick={handleJoin}
           size="lg"