fix(HomePage): 修复课程分类和已购标识的条件渲染问题

 <!--
  * @Date: 2025-03-20 19:55:21
  * @LastEditors: hookehuyr hookehuyr@gmail.com
- * @LastEditTime: 2025-11-11 16:29:22
+ * @LastEditTime: 2025-11-11 17:18:13
  * @FilePath: /mlaj/src/views/HomePage.vue
  * @Description: 美乐爱觉教育首页组件
  *
@@ -208,7 +208,7 @@
                   已购
                 </div>
                 <div class="absolute inset-0 bg-gradient-to-b from-transparent via-black/20 to-black/60 flex flex-col justify-end p-4">
-                  <div class="bg-amber-500/90 text-white px-2 py-1 rounded-full text-xs font-medium inline-block w-fit mb-1">
+                  <div v-if="course.category" class="bg-amber-500/90 text-white px-2 py-1 rounded-full text-xs font-medium inline-block w-fit mb-1">
                     {{ course.category }}
                   </div>
                   <h2 class="text-2xl font-bold text-white drop-shadow-md">{{ course.title }}</h2>
@@ -316,7 +316,7 @@
                     />
                     <!-- 已购标识 -->
                     <div
-                      v-if="item.is_buy"
+                      v-if="item?.is_buy"
                       class="absolute top-0 left-0 bg-orange-500 text-white text-xs px-2 py-1 rounded-br-lg font-medium"
                       style="background-color: rgba(249, 115, 22, 0.85)"
                     >