Here's the work flow to find and download an audio book:
1. Open app
2. Sign in
3. Search for audio book
4. Click on the desired result
5. Get transferred to web browser and this app web page
6. Sign in again
7. Place a hold
When the book becomes available
1. Open app
2. Navigate 3 pages deep to find the available book
3. Click the book to start the download
4. Get transferred to web browser and this app web page
5. Sign in again
6. The page says "book not available". Ignore that
7. Choose download format
8. Now a button appears to start the download. Click it.
9. Get transferred to the overdrive app
10. Sign in again
11. Finally start the download.
You can do all of this, including signing in 3 times, without ever leaving the Overdrive app. So, I see no point in this library app at all. Just use Overdrive, or log into your account in the web browser.