I am an avid user of iBooks, and I hope I can be somewhat helpful. Because I am new to Stack Exchange, I am unable to ask questions/comments on your original post, therefore some of this information may be irrelevant to you.
You mentioned that on your iPad and iPhone, you have the settings set to sync across devices. To clarify, click Settings > iBooks; make sure Sync Bookmarks & Notes and Sync Collections are green. It sounds like you have this already, so then...
Click Settings > Your name at the top > iCloud. Make sure iBooks is still marked green. Make sure iCloud Drive is also green.
On your Mac, open up iBooks. At the top menu bar, click Store > Authorize this computer.. this should ensure your computer can use anything added from iTunes/iBooks store. Also, click Sign In in the same menu setting (Store). Make sure your Apple ID is signed in.
Click the Apple icon at the top left of your screen and hit System Preferences. Click iCloud. Make sure your account is signed in. make sure iCloud Drive is on, and click settings next to it.
If iBooks was open, quit/force quit it. After it quits, open it. It may prompt you, "do you want to use iCloud sync?" If it does, say yes. Click iBooks > Preferences > General, make sure "sync across all devices is checked."
Your items will have a cloud icon on them. A cloud with a solid lining indicates the book is fully in the cloud and downloadable; a cloud with a dotted lining indicates the item is being uploaded into the cloud.
I believe the issue is with your iCloud Drive. iBooks purchases sync with your Apple ID, and technically other stuff you add does as well, but the other items, from my understanding, actually live in your iCloud Drive. You also may need to update your Mac.. sometimes syncing is weird with older stuff (you said Sierra; not sure if High Sierra or old Sierra). I am not sure this information will be helpful to you.
Also, this might be helpful. I apologize if all of these are things you have already done, but since I am new, I am unable to ask you questions yet. Good luck. I assume I can edit this answer if everything else fails... I do not have my Mac with me at work today, so I can't view my own settings. I can look when I get home if it would be beneficial.