Can the cart page suggest something to add?

Yes. Display → Cart Suggestions shows a few products under the bar on the cart page, each priced to get the cart to free shipping on its own and each with an Add to cart button. They come from the categories of the products in the cart, from categories you choose, or from products you choose, best sellers first, and every product gets a card before any gets a second. Adding one moves the bar without a page load, as long as WooCommerce's Enable AJAX add to cart buttons on archives is on or the cart page uses the Cart block, and the suggestions go once shipping is free. It is on for new installs; a shop that had the plugin before sees it suggested on the Dashboard, when On the cart page is on.