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/views/AiPlatformsView.vue

@@ -29,13 +29,6 @@ const aiAccounts = computed(() =>
   ),
 )
 
-const overview = computed(() => ({
-  configuredPlatforms: desktopMonitoringMediaCatalog.length,
-  bound: aiAccounts.value.length,
-  live: aiAccounts.value.filter((item) => item.health === 'live').length,
-  onlineClients: snapshot.value?.summary.onlineClients ?? 0,
-}))
-
 const platformCards = computed(() =>
   desktopMonitoringMediaCatalog.map((platform) => {
     const matched = aiAccounts.value.filter((account) => account.platform === platform.id)
@@ -47,6 +40,17 @@ const platformCards = computed(() =>
   }),
 )
 
+function isLocallyAuthorized(account: AccountRow | null): boolean {
+  return account?.authState === 'active'
+}
+
+const overview = computed(() => ({
+  configuredPlatforms: desktopMonitoringMediaCatalog.length,
+  authorized: platformCards.value.filter((platform) => isLocallyAuthorized(platform.account))
+    .length,
+  onlineClients: snapshot.value?.summary.onlineClients ?? 0,
+}))
+
 function authLabel(account: AccountRow | null) {
   if (!account) {
     return '未绑定'
@@ -258,13 +262,9 @@ async function unbindPlatform(account: AccountRow) {
           <div class="stat-label">支持平台</div>
           <div class="stat-value">{{ overview.configuredPlatforms }}</div>
         </div>
-        <div class="stat-card">
-          <div class="stat-label">已绑定</div>
-          <div class="stat-value">{{ overview.bound }}</div>
-        </div>
         <div class="stat-card">
           <div class="stat-label">授权正常</div>
-          <div class="stat-value">{{ overview.live }}</div>
+          <div class="stat-value">{{ overview.authorized }}</div>
         </div>
         <div class="stat-card">
           <div class="stat-label">在线客户端</div>