Exclude category shop page, but show in search results

Hi there,

I excluded a category on the main shop page with the function as explained on WC:

/**
 * Exclude products from a particular category on the shop page
 */
function custom_pre_get_posts_query( $q ) {

    $tax_query = (array) $q->get( 'tax_query' );

    $tax_query[] = array(
           'taxonomy' => 'product_cat',
           'field' => 'slug',
           'terms' => array( 'soldproducts' ), // Don't display sold products on the shop page.
           'operator' => 'NOT IN'
    );

    $q->set( 'tax_query', $tax_query );

}
add_action( 'woocommerce_product_query', 'custom_pre_get_posts_query' );

So far so good, but as of this the products in this category don’t also show up in a search in WC.

Is there a way to:
1. show the products in this category “soldproducts” in the WC search results, or
2. make a seperate search function for the “soldproducts”?

Thank you.