I see that you have an older model iPad which can only be updated to iOS 9.3.5. You've also noticed the current version of iTunes is now focusing on music, movies and such, you're not sure how to retrieve the iBooks you've purchased. I'm happy to help.
iTunes for Mac: Sync contacts, calendars, and other info with iPod, iPhone, or iPad -- If your iBooks are located in your iTunes library on a Mac or PC, you can sync them to your iPad.
Redownload music, movies, TV shows, apps, and books from the iTunes Store, iBooks Store, and App Store -- If you're not able to sync them through iTunes, you can redownload those books.