No, we are not deleting products in Shopify / Woocommerce / Shopify / Magento 2 and that is done intentionally. We think deleting product is dangerous features for below reasons:
Odoo is a warehouse system. Many employees working in Odoo in some cases even do not know that another e-Commerce system exists. And that their actions can influence another system.
Prestashop is customer-facing system and in most cases marketing team is doing beautiful descriptions inside it. Sometimes marketing team may also even might not know about Odoo.
So imagine now you by accident delete the product in Odoo. Then all work done by marketing will disappear. ANd product will disappear on the website also. So that is why we do not delete products.
Instead of deleting you need to use “Archive“ function in Odoo. So product will be hidden from Odoo interface.
That corresponds to the “active“ technical field on Odoo product. So if it’s synchronization is enabled (see this article), then Product will also be deactivated on eCommerce side.