How to Manage Audiobooks in a Post-iTunes World
You can move your audiobooks to the Books app, which offers a number of features for playback that are more appropriate for listening to spoken word. For example, you click buttons to skip ahead or back by 15 seconds, set a sleep timer, and more. However, these files are stored on your startup disk, and you may simply not have enough space on this disk[…]
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Or you can keep your audiobooks in your Music library. If you rip audiobook CDs, their files can stay in your Music library, and you can listen to them in the Music app, sync them to an iOS device, and even put them in your iCloud Music Library, if the bit rate is 96 kbps or above.
Previously:
At some point the iOS Books.app became quite untenable as an audiobook player for me, ranging from general unreliability, to the frustrations of getting them on there via iTunes. Actually, the waste of screen space on massive margins coupled with the selection of primarily 'wispy' fonts has made it untenable to me for text books also, but I digress.
There was a period where I used the Overcast file uploads for audiobooks I was listening to.
These days my favorite (iOS) solution for listening is GreenLit: https://apps.apple.com/us/app/greenlit-audiobook-player/id1360511601