This feature might become obsolete. I'm experimenting with a bot to manage all of the categories automatically. Dunno how well this will work but we'll try. What we can do with categories is very limited on Squarespace -- there is not an official way to automate anything. So I'm trying this experimental way.

Squarespace doesn't support categories when doing the automatic sync, but they use categories for organizing products and creating a navbar on Squarespace. Bookhead has a manual file export that allows you to map your book categories to products on Squarespace. It's a workaround but it does the job. This feature could be better if a bookseller gets notified when a new category comes in, because that book would be synced without a category since the categories is a manual process.