Variations products on shop page

Hello,

i’m trying to query all my products together with products variations for each categories i have. I would like to have 4 products for category on shop page

Example:

 $cats = get_terms( ['taxonomy' => 'product_cat', 'parent' => 0] );

foreach( $cats as ?$cat){

? ? ? ? $product_args = array(

? ? ? ? ? ? 'posts_per_page' => 4,

? ? ? ? ? ? 'post_status' => array('publish'),

? ? ? ? ? ? 'post_type' => array('product', 'product_variation'),

? ? ? ? ? ? 'orderby' => 'ID',

? ? ? ? ? ? 'suppress_filters' => false,

? ? ? ? ? ? 'orderby' => 'title',

? ? ? ? ? );

? ? ? ? ? if (!empty($cats)) {

? ? ? ? ? ? $product_args['tax_query'] = array(

? ? ? ? ? ? ? ?array(

? ? ? ? ? ? ? ? ?'taxonomy' => 'product_cat',

? ? ? ? ? ? ? ? ?'field' => 'term_id',

? ? ? ? ? ? ? ? ?'terms' => array( $cat->term_id ),

? ? ? ? ? ? ? ? ?'operator' => 'IN',

? ? ? ? ? ? ));

? ? ? ? ? }

? ? ? ? ? $query = new WP_Query( $product_args);

? ? ? ? ? ? woocommerce_product_loop_start();

? ? ? ? ? if ( wc_get_loop_prop( 'total' ) ) {

? ? ? ? ? ? while ( $query->have_posts() ) {

? ? ? ? ? ? ? ? $query->the_post();

? ? ? ? ? ? ? ?  do_action( 'woocommerce_shop_loop' );

? ? ? ? ? ? ? ? wc_get_template_part( 'content', 'product' );

? ? ? ? ? ? }

? ? ? ? }

? ? ? ? wp_reset_postdata();

? ? ? ? woocommerce_product_loop_end();

? ? ? } 

With this, i have 4 products for categories, but i don’t see the single variations, example my hoodie green and my hoodie blue.

What do you suggest to do ?

Thank you

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