Books did not successfully transfer to my new iPhone13

I recently upgraded from an iPhone6S+ to an iPhone13. I did the transfer to the new phone myself, and it seemed to go smoothly. Maybe a week later, I opened Books on the new phone to find a weird scramble: only 4 files show up in Books, 3 are Apple-generated (e.g., manual for iPhone) and only 1 from the many .pdf files I have added to Books (things like maps, etc.).

My 2 Macs still have all the items I have added to Books - 4 books, 1 series & 87 .pdfs

Digging further into the iPhone, I found that when I go through Settings to iCloud > iCloud Storage, the Books app shows up twice, one with a minimal 3.4KB, and one with 278.5MB of data. It seems like the 3KB one must be what my phone is using as the library, while the massively larger one is probably the full library I expected.

I don't see any way to direct Books to use the larger library. Manage Storage only offers to "delete data" or "delete documents & data", and explains that either action will affect all my connected devices. Makes it sound like that choice will delete all my books library files, which I definitely do not want.

So what can I do to try to get my library files in order in my iPhone's Books app, without screwing up the library (libraries?) used by my other Mac devices?

Thanks in advance for any suggestions,

John