feat(workspace): replace supported platform count with bound media account count

The "platforms" stat tile was a constant (5) that never reflected what the
tenant actually had set up. Drop SupportedPlatformCount from the workspace
overview API/domain/shared-types and have admin-web compute a bound media
account count from the desktop accounts list, filtered through a new
isMediaPublishAccount helper that excludes deleted rows and AI-only
platforms (yuanbao/kimi/wenxin/deepseek/doubao/qwen).

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

apps/admin-web/src/lib/publish-account-cards.ts

@@ -4,6 +4,7 @@ import { resolveApiURL } from "@/lib/api";
 import { resolveAccountCheckedAt, resolveAccountHealth } from "@/lib/desktop-account-runtime";
 import {
   getPublishPlatformMeta,
+  isMediaPublishAccount,
   isPublishPlatformId,
   normalizePublishPlatformId,
 } from "@/lib/publish-platforms";
@@ -65,7 +66,7 @@ export function buildPublishAccountCards(
 
   return accounts
     .filter((account) => {
-      if (account.deleted_at) {
+      if (!isMediaPublishAccount(account)) {
         return false;
       }
       const platformId = normalizePublishPlatformId(account.platform);

apps/admin-web/src/lib/publish-platforms.ts

@@ -25,9 +25,19 @@ const platformCatalog: Record<string, Omit<PublishPlatformOption, "accountLabel"
   dongchedi: { id: "dongchedi", name: "懂车帝", shortName: "懂", accent: "#fadb14" },
 };
 
+const aiPlatformIds = new Set(["yuanbao", "kimi", "wenxin", "deepseek", "doubao", "qwen"]);
+
+export function isAIPlatformId(platformId?: string | null): boolean {
+  return aiPlatformIds.has(normalizePublishPlatformId(platformId));
+}
+
 export function isPublishPlatformId(platformId?: string | null): boolean {
   const normalized = normalizePublishPlatformId(platformId);
-  return Boolean(normalized) && normalized in platformCatalog;
+  return Boolean(normalized) && !isAIPlatformId(normalized) && normalized in platformCatalog;
+}
+
+export function isMediaPublishAccount(account: DesktopAccountInfo): boolean {
+  return !account.deleted_at && isPublishPlatformId(account.platform);
 }
 
 export function getPublishPlatformMeta(platformId: string): Omit<PublishPlatformOption, "accountLabel" | "bound"> {