build: auto-generate public directory

Author: myoshi2891

public/index.html

@@ -797,7 +797,7 @@ <h1 class="site-title">
 
     <footer>
         <span class="footer-icon">🧪</span>
-        Generated on 2026-02-28 06:00:55 UTC
+        Generated on 2026-02-28 06:01:25 UTC
     </footer>
 
     <script>