How do I go to the next page in Books without the sliding animation bit?

Perhaps from the " Apple Books User Guide "

and an excerpt for that link above

Show one or two pages in a book

1. In the Books app  on your Mac, click Books (or another collection) in the sidebar, then double-click a book.
2. Drag the window’s sides left or right until you see one or two pages

Turn off pagination in a book

You can scroll through a book instead of turning the pages.

1. In the Books app  on your Mac, click Books (or another collection) in the sidebar, then double-click a book.
2. Move the pointer to the top of the book, click the Appearance button , then turn on Vertical Scrolling or Horizontal Scrolling, depending on the format of the book.
3. If the Appearance button isn’t available, choose View > Vertical Scrolling or Horizontal Scrolling.

Then have a few suggestions ;

1 - Get Support Choose a product and we’ll find you the best solution.Start now and open an Apple Support Ticket as they are Apple Employees to deal will these types of issues . 

2 - Product Feedback - Apple and make it known to Apple regarding this ongoing issue