feat: fix recording save and add publish/unpublish support

- Fix broken fetch("/api/sexy/recordings") → use createRecording GraphQL service
- Round duration to integer before sending (GraphQL Int type)
- Add updateRecording mutation to services
- Add publish/unpublish buttons to RecordingCard (draft ↔ published)
- Remove "Go to Play" button from recordings page header
- Add publish/unpublish i18n keys

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

packages/frontend/src/lib/i18n/locales/en.ts

@@ -151,6 +151,10 @@ export default {
       delete_confirm: "Are you sure you want to delete this recording?",
       delete_success: "Recording deleted successfully",
       delete_error: "Failed to delete recording",
+      publish_success: "Recording published successfully",
+      publish_error: "Failed to publish recording",
+      unpublish_success: "Recording unpublished",
+      unpublish_error: "Failed to unpublish recording",
     },
   },
   recording_card: {
@@ -161,6 +165,8 @@ export default {
     status_draft: "Draft",
     status_published: "Published",
     play: "Play",
+    publish: "Publish",
+    unpublish: "Unpublish",
     edit: "Edit",
     delete: "Delete",
     public: "Public",