feat(manascore): add live uptime badges from status.mana.how

- generate-status-page.sh now also writes status.json alongside index.html
  Format: { updated, summary: {up, total}, services: { appName: bool } }
- nginx status.mana.how serves status.json with CORS headers (public read)
  and explicit location block to avoid rewrite to index.html
- ManaScore index page fetches status.json client-side on load and
  injects green ● LIVE / red ● DOWN badge next to each app's status chip

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

docker/nginx/landings.conf

@@ -118,10 +118,22 @@ server {
     add_header X-Content-Type-Options "nosniff" always;
     add_header Cache-Control "no-store" always;
 
+    # Allow ManaScore page to fetch status.json
+    add_header Access-Control-Allow-Origin "*" always;
+    add_header Access-Control-Allow-Methods "GET" always;
+
     location / {
         try_files $uri /index.html;
     }
 
+    # Serve status.json directly (do not rewrite to index.html)
+    location = /status.json {
+        add_header Content-Type "application/json" always;
+        add_header Cache-Control "no-store" always;
+        add_header Access-Control-Allow-Origin "*" always;
+        try_files $uri =404;
+    }
+
     location /health {
         access_log off;
         return 200 "healthy\n";