Can Essential Upsell offers appear inside the Essential Cart Drawer? (Essential Upsell app)

Yes. Essential Upsell can show offers inside the Essential Cart Drawer. The offer appears at the cart upsell position set in the drawer.

The Essential Cart Drawer app also has its own Upsells section. That is a separate feature. Changes made there do not configure Essential Upsell offers. To show an Essential Upsell offer in the cart, set the offer's placement to Cart page in Essential Upsell.

After you save, open the cart drawer on your storefront and check that the offer appears where you expect. If it does not appear, check that both apps are turned on in Online Store → Themes → Customize → App embeds.