Re: "Unable to remove/re-add audiobooks on iPhone 13 in iTunes"
Seems the Books app replaced iTunes for audiobooks quite some time ago.
(Songs are in the Music app, movies in the Apple TV app, podcasts in the Podcasts app)
Listen to audiobooks in the Books app on iPhone - Apple Support
Eg: says:
If you can't find an audiobook purchase
If you've bought an audiobook and can't find it in your Library, redownload your audiobook.
Organize books in the Books app on iPhone - Apple Support
Eg; Says:
"You can remove or hide books, audiobooks, and PDFs from Home, Library, and your library collections.
- Go to the Books app
on your iPhone. - Navigate to a book or audiobook you want to remove, then tap
below the cover. - Tap Remove, then choose an option.
- Note: If you choose Remove Download, the content and data associated with the title are no longer stored on your iPhone. To redownload the title, tap
, then tap Download. If you choose Hide Book, the book won’t appear in your library or collections. To unhide books and audiobooks, tap Home, tap your account icon, then tap Manage Hidden Purchases.
You can automatically remove downloads from your iPhone after you finish a book. Tap Library, then tap
at the top right of the screen. Tap Remove Downloads, then tap Automatically When Finished."