Ajax call in wordpress not working for subscriber user in front site

For non-admin users to be able to use an ajax function, you need to also include a second hook using wp_ajax_nopriv

So right after this:

add_action('wp_ajax_add_category_bookly', 'add_category_bookly_callback');

you should include this:

add_action('wp_ajax_nopriv_add_category_bookly', 'add_category_bookly_callback');