The problem has been solved. The Books Team, <iwork@apple.com>, kindly sent me an email three days ago; I quote
We’re looking in to the issue reported in your Apple Discussion Forums post. We’d like to have a better understanding about what happened, but need more information.
Could you try the following:
- Delete the books and re-sync them from the desktop using iTunes on macOS 10.14.x or older or Finder on macOS 10.15 or newer
Please let us know if this resolves your issue. If this does not or you are experiencing a different issue, could you please provide a screen recording or video that demonstrates your issue?
This afternoon I made three out of the four audiobooks usable again working locally on the iPhone by "right clicking" each in what I guess in English is called the "Downloaded" section, and then choosing "Remove". Afterwards they were marked with a "Cloud icon", and then that book were listenable - I guess "from the cloud".
Unfortunately one of the books - the book I was listening to when upgrading iOS - disappeared from the iPhone when trying the above. This could of course be my mistake. For this book I installed iTunes on my Windows laptop and then synchronized the iPhone from an old backup of my iTunes library.
So everything is now fine again once more, and I am currently following Merry and the Riders of Rohan arriving at Dunharrow.
Kind regards,
Hans Henrik Krohn
P.S.: The recent update to iOS 13.4.1 didn't change anything.
