refactor(desktop): show authorized AI platforms count on shell

The shell badge and the AI Platforms overview now report platforms
whose binding is locally authorized (authState=active) instead of the
total bound platforms, so the number reflects how many monitoring
sources are actually usable.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

apps/desktop-client/src/renderer/components/DesktopShell.vue

@@ -30,7 +30,9 @@ const navItems = computed(() => {
   const data = snapshot.value
   const accounts = data?.accounts ?? []
   const publishIDs = new Set(desktopPublishMediaCatalog.map((item) => item.id))
-  const monitoringIDs = new Set(desktopMonitoringMediaCatalog.map((item) => item.id))
+  const authorizedMonitoringCount = desktopMonitoringMediaCatalog.filter((platform) =>
+    accounts.find((account) => account.platform === platform.id)?.authState === 'active',
+  ).length
 
   return [
     {
@@ -57,8 +59,8 @@ const navItems = computed(() => {
     {
       to: '/ai-platforms',
       title: 'AI 平台',
-      description: 'AI 平台一平台一绑定，按卡片查看状态与归属',
-      count: accounts.filter((item) => monitoringIDs.has(item.platform)).length,
+      description: 'AI 平台一平台一授权，按卡片查看状态与归属',
+      count: authorizedMonitoringCount,
       icon: RobotOutlined,
     },
   ]