You are welcome!
Correct – The results page design/layout is out of the scope of the search as it is controlled by the theme. Usually it is passed to the search.php and then whatever is required in that file, it varies for every theme. In your case it is very likely the content-search.php as you pointed out.
To get the thumbnail URL you may have to use something like:
wp_get_attachment_image_url( get_the_ID() );