Are there any apps that offer "last-step upsell/cross-sell" which can show an item on a popup after clicking on the "Checkout" button?

Up-selling and cross-selling your products is an effective strategy to boost your sales conversion rates.

"ReConvert Upsell & Cross Sell" and "Last Upsell — Post‑Purchase" are two top-ranked apps on the list for post-purchase upselling and cross-selling. They offer a free plan/trial, so testing them out is risk-free. You can also try using Selly to create customized popups.

Consider looking at Shopify Apps that specialise in pop-ups rather than cross or up-selling as you may find that they offer exactly what you are looking for. Take a look at 'SmartPopup: Promotion Popup' by Secomapp and 'Justuno Pop Ups Bundle Upsell' by Justuno which are either free or have a free plan available.