How do I add an ePub to my iPad

I have an ePub which I bought outside of the Book Store, and on which there is no DRM. It is sitting on my iMac, running MacOS Big Sur.

I can double click on the ePub and open it in the Books App. From there I can add it to one of my collections. The question is how do I add it to my iPad from there?

As of Catalina, you’re supposed to do this sort of thing in the Finder. Indeed I can see my iPad, and select the Books tab. However, the list of books only shows a few dozen books, when my iPad definitely has hundreds. The list of books doesn’t show my new books, certainly not my collections. Thus there is no check box for me to select and then sync.

What do I do now?

Just send the book via AirDrop to your iPad, then click share and after that select the Books app.