添加主页功能，支持加载和展示首页数据，包括链接和推荐应用列表

src/components/AppHeader.vue

@@ -10,7 +10,7 @@
         >
           <i class="fas fa-bars"></i>
         </button>
-        <TopActions @update="$emit('update')" @list="$emit('list')" />
+        <TopActions @update="$emit('update')" @list="$emit('list')" @open-install-settings="$emit('open-install-settings')" />
       </div>
       <div class="w-full flex-1">
         <label for="searchBox" class="sr-only">搜索应用</label>
@@ -24,12 +24,13 @@
             class="w-full rounded-2xl border border-slate-200/70 bg-white/80 py-3 pl-12 pr-4 text-sm text-slate-700 shadow-sm outline-none transition placeholder:text-slate-400 focus:border-brand/50 focus:ring-4 focus:ring-brand/10 dark:border-slate-800/70 dark:bg-slate-900/60 dark:text-slate-200"
             placeholder="搜索应用名 / 包名 / 标签，按回车键搜索"
             @keydown.enter="handleSearch"
+            @focus="handleSearchFocus"
           />
         </div>
       </div>
     </div>
-    <div class="text-sm text-slate-500 dark:text-slate-400" id="currentCount">
-      共 {{ appsCount }} 个应用 · 在任何主流 Linux 发行上安装应用
+    <div v-if="activeCategory !== 'home'" class="text-sm text-slate-500 dark:text-slate-400" id="currentCount">
+      共 {{ appsCount }} 个应用 
     </div>
   </div>
 </template>
@@ -48,6 +49,8 @@ const emit = defineEmits<{
   (e: "update-search", query: string): void;
   (e: "update"): void;
   (e: "list"): void;
+  (e: "search-focus"): void;
+  (e: "open-install-settings"): void;
   (e: "toggle-sidebar"): void;
 }>();
 
@@ -57,6 +60,10 @@ const handleSearch = () => {
   emit("update-search", localSearchQuery.value);
 };
 
+const handleSearchFocus = () => {
+  emit("search-focus");
+};
+
 watch(
   () => props.searchQuery,
   (newVal) => {