How do I mark my books as read in iBooks?

I would suggest a twofold approach...

• Add a "Finished" Collection [see Organize your Library > About iBooks - Apple Support ]
  • Move your read books to it
  • SYNC/Backup
• Delete the copy from your device
  iBooks: Tips for managing your iBooks library and storage on iOS devices - Apple Support
  [from near the bottom]
  To free up storage on your device while preserving your library organization, tap Delete This Copy. The copy of the book on that iOS device will be removed, but the cover of the book will remain in your iBooks library with a cloud icon visible in the upper corner. To download the book again, just tap the book cover.

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😉 ! you gotta read the linked articles ! 😀

The first part of what I said:

• Add a "Finished" Collection [see Organize your Library > About iBooks - Apple Support ]

.

For your convenience:

Organize your library

You can sort books in iBooks by switching to List view and tapping Most Recent, Titles, Authors, or Categories.

You can also organize your books in these ways:

• A grid or list view.
• Specific collections based on a topic. For example, you can put all your books and PDFs related to your work in a single collection.

To change or add new Collections, tap the Collections button, or the name of the collection on your iPhone or iPod touch. To rearrange books in your iBooks collections, touch and hold a book, then move it where you want it. (You can't rearrange books in the All Books collection.)

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