feat(site): add Mux health check action (#542)

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

site/src/pages/api/health/mux.ts

@@ -0,0 +1,14 @@
+import { actions } from 'astro:actions';
+import type { APIRoute } from 'astro';
+
+export const prerender = false;
+
+export const GET: APIRoute = async (context) => {
+  const { data, error } = await context.callAction(actions.mux.health, {});
+
+  if (error) {
+    return Response.json({ ok: false, error: error.message }, { status: 502 });
+  }
+
+  return Response.json(data);
+};