Q: how to save a photos book spread page to pdf?

this preview pdf should work - Preview a print project in Photos, iPhoto, or Aperture to avoid issues - Apple Support

LN

Since they print from the pdf that is created by Photos printing the full width spread as one large page is probably done to eliminate any gutter issues at the binding when it's assembled.

Do you want each side to be as an individual page in the PDF file?

there is no print command from photos book. Only save as PDFs or preview.

There is. Simply select the book and use the key combination ⌘P for the command "File > Print". In the Print panel you can click the PFD button in the lower left corner.

But the results will be worse.  If you create the PDF this way the spread page will be centered on one single page and cropped.