Hi,
It is kind of intentional (so it only clears the prhase), as it is not completely possible to reset the elementor widget state to it’s original form. There is however a custom code I can suggest, that will trigger an empty search when clicking the close button.
Try adding this custom code to the functions.php in your theme/child theme directory. Before editing, please make sure to have a full site back-up just in case!
add_action('wp_footer', 'asp_trigger_search_on_close');
function asp_trigger_search_on_close() {
?>
<script>
jQuery(function($){
$('.proclose svg').on('click touchend', function(e){
var $e = $(this).closest('.asp_w');
setTimeout(function(){
ASP.api($e.data('id'), $e.data('instance'), 'searchFor');
}, 250);
});
});
</script>
<?php
}