You can execute this javascript to reload the page:
window.location.assign(window.location.href);
But something needs to trigger it. Add an event listener perhaps?
To get your script loaded call wp_enqueue_script() from a callback hooked to “admin_enqueue_scripts” action.
The problem will be the browser will reload from its cache instead of fetching the page from the server. When the page initially loads we need to send a Cache-Control header telling the browser not to cache the page. This can be added in the “wp_headers” filter, but depending on several factors, this may not work without further adjustments to other headers, .htaccess, httpd.conf, etc.