We apologize for the inconvenience.
I have checked your website and found that the issue is related to the .htaccess file. Search Engine Friendly (SEF) URLs are enabled on your Joomla site, but the current .htaccess file does not contain the proper rewrite rules required to handle SEF URLs correctly after moving the site to a different directory.
Please replace/update the .htaccess file with the correct Joomla .htaccess code. You can obtain the original .htaccess file from a fresh Joomla installation and upload it to your site's root directory.
As a temporary workaround, if you disable Search Engine Friendly URLs from Joomla Global Configuration → Site → SEO, the menu links and homepage buttons should work correctly.
Once the proper .htaccess file is in place, you can re-enable SEF URLs and the links should work as expected.
Thank you for your patience and understanding.