fix(admin): Support entry in sidebar + awaiting-admin badge

The /admin/support page existed but was invisible from the panel — sidebar
NAV array didn't list it. Adds Support as the 2nd nav item (right after
Overview, since unanswered tickets are the most-time-sensitive thing an
admin checks). Sidebar polls /v1/admin/support/counts every 30s and renders
an amber count badge next to the entry when tickets are awaiting_admin.

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

apps/api/src/routes/support.ts

@@ -3,6 +3,7 @@ import {
   createDb,
   desc,
   eq,
+  sql,
   supportMessages,
   supportTickets,
   users,
@@ -182,6 +183,18 @@ export async function supportRoutes(app: FastifyInstance): Promise<void> {
   });
 
   // ─── Admin-side ────────────────────────────────────────────────────────
+  app.get(
+    '/v1/admin/support/counts',
+    { preHandler: requireAdmin },
+    async (_req, reply) => {
+      const [row] = await db
+        .select({ count: sql<number>`count(*)::int` })
+        .from(supportTickets)
+        .where(eq(supportTickets.status, 'awaiting_admin'));
+      return reply.send({ awaitingAdmin: row?.count ?? 0 });
+    },
+  );
+
   app.get(
     '/v1/admin/support/tickets',
     { preHandler: requireAdmin },

apps/web/app/admin/layout.tsx

@@ -5,6 +5,7 @@ import { usePathname, useRouter } from 'next/navigation';
 import { useEffect, useState } from 'react';
 import {
   LayoutGrid,
+  LifeBuoy,
   Users,
   Building2,
   Server,
@@ -29,6 +30,7 @@ interface MeUser {
 
 const NAV: { href: string; label: string; icon: React.ComponentType<{ size?: number }> }[] = [
   { href: '/admin', label: 'Overview', icon: LayoutGrid },
+  { href: '/admin/support', label: 'Support', icon: LifeBuoy },
   { href: '/admin/users', label: 'Users', icon: Users },
   { href: '/admin/orgs', label: 'Organizations', icon: Building2 },
   { href: '/admin/servers', label: 'MCP servers', icon: Server },
@@ -45,6 +47,7 @@ export default function AdminLayout({ children }: { children: React.ReactNode })
   const router = useRouter();
   const [user, setUser] = useState<MeUser | null>(null);
   const [authState, setAuthState] = useState<'checking' | 'ok' | 'forbidden'>('checking');
+  const [supportPending, setSupportPending] = useState(0);
 
   useEffect(() => {
     if (pathname === '/admin/login') {
@@ -63,6 +66,26 @@ export default function AdminLayout({ children }: { children: React.ReactNode })
       .catch(() => setAuthState('forbidden'));
   }, [pathname]);
 
+  // Poll support count every 30s so the sidebar badge stays fresh while admin
+  // is doing other work in the panel.
+  useEffect(() => {
+    if (authState !== 'ok' || pathname === '/admin/login') return;
+    let cancelled = false;
+    const load = () => {
+      apiFetch<{ awaitingAdmin: number }>('/v1/admin/support/counts')
+        .then((r) => {
+          if (!cancelled) setSupportPending(r.awaitingAdmin);
+        })
+        .catch(() => undefined);
+    };
+    load();
+    const t = setInterval(load, 30_000);
+    return () => {
+      cancelled = true;
+      clearInterval(t);
+    };
+  }, [authState, pathname]);
+
   useEffect(() => {
     if (authState === 'forbidden' && pathname !== '/admin/login') {
       router.replace('/admin/login');
@@ -126,7 +149,12 @@ export default function AdminLayout({ children }: { children: React.ReactNode })
                     )}
                   >
                     <Icon size={13} />
-                    {item.label}
+                    <span className="flex-1">{item.label}</span>
+                    {item.href === '/admin/support' && supportPending > 0 && (
+                      <span className="mono inline-flex h-4 min-w-4 items-center justify-center rounded-full bg-amber-500/30 px-1 text-[10px] font-semibold text-amber-300">
+                        {supportPending}
+                      </span>
+                    )}
                   </Link>
                 </li>
               );