If your Books aren't syncing via iCloud, make sure your Books settings has Syncing / iCloud Drive turned on
I put some EPUB files into the Books app on my Mac. Even though my Mac, my iPhone, and my iPad all have iCloud syncing for Books turned on, the books were not appearing on the mobile devices. The new category that I created for them did show up on the iPhone and iPad, but it was empty. (All devices are running their current OS as of now, January 2024.)
I went into the iCloud settings and turned Books syncing off and on again a few times on all of the devices, but that didn't solve the problem.
Finally I noticed that on iPhone/iPad, the Settings app has a separate section for Books. In there, there's a "Syncing" section, where I had "iCloud Drive" turned off. Turning that setting on resulted in my books immediately appearing on the device.
I'm sharing this here in case it helps anyone else.