In 2022, Apple's changed its OS and took away your ability to download MP3 audiobooks directly to the iPhone and iPad's native audiobook reader, iBooks. You can use iMusic, but the chapter order is often scrambled, and you lose the controls you want in an audiobook app (reading speed, replay last 10 seconds, etc.).
Here's the workaround: Go to the App Store and search using this string: "MP3 audiobook player". Choose a free or paid app that works on your device. When you have the app installed, download the MP3 files using that app's downloading menu.
This isn't ideal, but Apple's software decisions are outside our control. (They didn't ask us!)
At some point in the not-too-distant future, many of our audiobooks will be available for purchase from Apple within iBooks. At present, and probably always, you will need to have the 3rd party MP3 app to listen to any previously purchased MP3 content.