You can create a new custom column in admin product list page. We can use manage_edit-product_columns filter hook and manage_product_posts_custom_column action hook for create new column.

“Primary category” is not a default woocommerce feature. It is comes from yoast seo plugin. This field is stored in postmeta table with “_yoast_wpseo_primary_product_cat” meta_key.

Add the following code in functions.php of your child theme.

// ==== add primary category column to products list page ====
add_filter('manage_edit-product_columns', 'wp_wiki_add_primary_category_column', 10);
function wp_wiki_add_primary_category_column($columns)
{
    $new_columns = array();
    foreach ($columns as $column_name => $column_info) {
        $new_columns[$column_name] = $column_info;
        if ('product_cat' === $column_name) {
            // Add New column after category column
            $new_columns['primary_cat'] = __('Primary Category', 'my_textdomain');
        }
    }
    return $new_columns;
}

// ==== add primary category column content to new column ====
add_action('manage_product_posts_custom_column', 'wp_wiki_add_primary_category_column_content');
function wp_wiki_add_primary_category_column_content($column)
{
    global $post;
    if ('primary_cat' === $column) :
        $taxonomy = 'product_cat';
        $primary_cat_id = get_post_meta($post->ID, '_yoast_wpseo_primary_product_cat', true);
        $primary_cat_name = '';
        if ($primary_cat_id) :
            $primary_cat = get_term($primary_cat_id, $taxonomy);
            if (isset($primary_cat->name)) :
                $primary_cat_name = $primary_cat->name;
            endif;
        endif;
        echo $primary_cat_name;
    endif;
}

This will create a new column with “Primary Category” as shown in the below screenshot.