There is a way to export highlights, if you can get a spare older iPad running iPadOS 15. The overall idea is, sync the newer iPad Books to iCloud Drive, then sync the older iPad. From the old iPad you can email your notes out.
Here's the process, step by step:
1. Make sure the old iPad isn't syncing.
On the older iPad, running iPadOS 15:
Settings -> Books -> Syncing -> iCloud Drive -> Off
2. Make a full back up of your newer iPad and Library in case there are any problems in the sync process.
Be careful! You want to make sure the new iPad's books and highlights get copied to the old iPad, not the other way around! It's probably safest if the iPadOS 15 iPad starts with an empty Books Library, maybe even has just had a factory reset.
3. Turn on syncing on the new iPad, running iPadOS 16:
Settings -> Books -> Syncing -> iCloud Drive -> On
Wait until it starts showing progress on uploading your books and PDFs. I think it took a few minutes for me to see it start.
Then wait till it's says it's finished. I think it took around 10-15 minutes.
4. Now that the new iPad has finished uploading all your Library, turn on syncing on the old iPadOS:
Settings -> Books -> Syncing -> iCloud Drive -> On
5. Wait for the old iPad to finish syncing.
It will show progress as it goes, and it will take a while to fully sync.
For me, 100 books took about 20-30 minutes.
6. Now export your books from the older iPadOS:
while reading a book:
table of contents icon -> Notes -> Share icon -> Edit Notes -> Select All -> Share -> Mail