Unfortunately we cannot automatically add the star rating to the product widget.
You must edit the widget product theme file (in folder [yourtheme]/woocommerce/content-widget-product.php, if there is no file please copy it over from the woocommerce plugin/templates folder, the full user guide is at https://docs.woocommerce.com/document/template-structure/ )
and add the following code under the product title to show the judgeme badge:
<?php echo do_shortcode('[jgm-preview-badge]');?>
And also remove the part of native woocmmerce rating if needed.