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I am wondering if you could take a random Apple Books EPUB book and then have a button to convert it to a Pages document.
Whatever I search on the community, it's all information about macOS which I don't use.
iPhone 12 Pro Max, iOS 17
Unfortunately, I think due to rights restriction there is no point to looking for any chance of exporting books. Probably due to keywords you mentioned you found information about import to Books by deprecated and not supported Mac app called iBook Authors, which was replaced by Pages functionality.
More information:
Transition from iBooks Author to Pages - Apple Support
How to convert an Apple Books book to Pages document
