Can I move, resize or hide the preorder badge? (Essent Preorder Back in Stock app)

Hide it: campaign → Content tab → untick Show preorder badge → Save.
Change its text or colours: campaign → Design tab → Badge → edit Badge text, Background colour and Text colour.
Move or resize it (for example top left instead of top right, bigger, square corners): this isn't a merchant setting. Click Reach out next to the badge settings or chat with support and tell us where you want it. We do it for free.
Show it on product pages only (not on the homepage or collection cards): ask support to hide it on those pages for your theme.

Why the badge shows on a collection card when only some sizes are on preorder

A collection card has no variant selected, so the badge shows if any variant of the product is on preorder. It can't be targeted per variant on collection pages. Your options are to hide it on collection pages or keep it.