Hi Jfpainter,
Welcome to the Apple Community.
You might want to check on the availability of Apple Media Services in your country,
to ensure Apple Books should be working soothly for you:
Availability of Apple Media Services – Apple Support
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Troubleshooting:
Apple's article: “If you can't connect to the App Store, iTunes Store or other Apple services”:
Try following these steps if you can't reliably connect to the Books app or services:
If you can't connect to the App Store, iTunes Store or other Apple services – Apple Support
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Re: Is there a way to back up all my books to apply to another app?
Seems there are several ways:
In the short term: Access your library across devices
You can keep your library and collections updated across all your devices where you’re signed in with the same Apple ID.
Go to Settings > [your name] > iCloud, turn on iCloud Drive, then turn on Books.
Or
Connect external storage devices to iPad – Apple Support
More:
How to: Use AirDrop on iPad to send items to nearby devices – Apple Support
Transfer files between iPad and your computer – Apple Support
How to back up your iPhone, iPad and iPod touch with your Mac – Apple Support
Back up and restore your iPhone or iPad to your Mac or to iCloud – Apple Support
All the best :-)