change global widget settings

hey everyone,
i am creating a ajax pagination plugin for the woocommerce products widget,
so when the user clicks the next page button, a request is sent to the backend and then queries the database for product posts:

$loop = new WP_Query( $products_args );

if ( $loop->have_posts() ) {

   echo "<ul class='products'>";

   while ( $loop->have_posts() ) : $loop->the_post();

        wc_get_template_part( 'content', 'product' );

    endwhile;

    echo "</ul>";

}

then as you can see, prints the template part content product.
but instead i would like to get a global widget i created with the right css and settings, with the queried posts.
i thought to output the shortcode of the global widget, but i don’t know how to change the query or posts inside.

thanks for the help.
(in the attached link you can see at the suggested products above the price a pagination on the left side, test it and see what is happening to the products. i need them to be as they where at the first place)

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