build: auto-generate public directory

Author: myoshi2891

public/index.html

@@ -785,7 +785,7 @@ <h1 class="site-title">
 
     <footer>
         <span class="footer-icon">🧪</span>
-        Generated on 2026-02-20 07:20:00 UTC
+        Generated on 2026-02-20 07:20:55 UTC
     </footer>
 
     <script>