Currently, Cross sell selected in the admin for products only affects the output of offered products on the cart page for cross-selling. This is a standard feature of WooCommerce.
Add settings in the theme to enable Cross sell output on the product page. And create a filter to display such products.
This will allow us to manage product offers more easily and flexibly, avoiding excessive custom code
Description of the difference between Related Products, Up-Sells and Cross-Sells: https://woocommerce.com/document/related-products-up-sells-and-cross-sells/