Refactor content status terminology and enhance cluster serializers with idea and content counts

frontend/src/pages/Writer/Content.tsx

@@ -8,7 +8,7 @@ import HTMLContentRenderer from '../../components/common/HTMLContentRenderer';
 const statusColors: Record<string, 'warning' | 'info' | 'success' | 'primary'> = {
   draft: 'warning',
   review: 'info',
-  published: 'success',
+  publish: 'success',
 };
 
 export default function Content() {
@@ -176,7 +176,7 @@ export default function Content() {
                         size="sm"
                         variant="light"
                       >
-                        {item.status?.replace('_', ' ') || 'draft'}
+                        {(item.status || 'draft').replace('_', ' ').replace(/^\w/, (c) => c.toUpperCase())}
                       </Badge>
                     </td>
                     <td className="px-5 py-4 align-top text-gray-600 dark:text-gray-400">