Q: Syncing/Transfering from iBooks to iTunes

I don't know how things are set up for e-books (this is the iTunes forum). I know things are fairly restrictive with iTunes because it is assumed what you have on an i-device is secondary to the master copy on a computer. For non-iTunes Store purchases you download things directly from the provider to the computer:

Your i-device was not designed for unique storage of your media. It is not a backup device and media transfer was planned with you maintaining a master copy of your media on a computer which is itself independently backed up against loss.  To use a device with a different setup you transfer the old library from a computer or a backup directly to the new setup, not the device to the library. Media syncing is one way, computer to device, updating the device content to the content on the computer, not updating or restoring content on a computer. The exception is iTunes Store purchases which can be transferred to a computer.

Redownload or transfer your iTunes Store purchases from an iPhone, iPad or iPod to a computer - https://support.apple.com/en-us/HT201267 - "This feature works only for content bought from the iTunes Store." As of iOS9 it no longer does apps which now must be re-downloaded directly from the Store.

For transferring other items from an i-device to a computer you will have to use third party commercial software.  See this document by turingtest2: Recovering your iTunes library from your iPod or iOS device - https://discussions.apple.com/docs/DOC-3991  Even this method may not fully recover what you had in the library originally. For example if in order to save space when syncing you had converted music files to a lower bitrate, or photos to a lower resolution, it is those lower quality files you will recover.

If you subscribe to Apple Music, tracks which are not part of content you have purchased or uploaded cannot be transferred and have to be downloaded directly from iCloud.

Does File > Devices > Transfer Purchases not copy them over to your Mac (that has always copied PDFs and/or epubs in the iBooks app, not just actual ibooks), and if your Mac is on Yosemite+ you then need to do File > Move Books From iTunes in its iBooks app to copy them over to that.

Everything I've found to help me says I have to go to the "Books" menu in iTunes and turn on the sync option. I remember doing this in the past when I had a similar issue, however that doesn't seem to be an option now. When I select my device in iTunes and look at all of the settings options "Books" is not an existing menu

The 'sync option' is for selecting and syncing books to a device from the computer, not to copy them off it. You aren't seeing something like :

Not sure how, or if, it will show if you are using iCloud Drive for iBooks (I'm not using it).