Prinitng a booklet in Pages

No worries! I'm sorry I wasn't able to help more with your problem, but I'm glad you got the page ordering sorted out. Not sure what to suggest about the shrinkage. It might be worth fiddling with the Scale to fit paper size setting in the Paper Handling section of the Print dialog:

EDIT: also try switching between A4 and A4 borderless and see if that has any effect.

Pages is a consumer-level word-processing/page layout program, and doesn't offer high-end options like print imposition and folding. Even with a more professionally-oriented program like InDesign, imposition is handled (at a cost) by third-party plugins and is not part of the base software.

The layout directions in pages are part of the standard macOS print dialog. They don't take account of the number of pages in the document, and they certainly don't rotate half the pages 180º and re-order them as would be required for true imposition.

With a certain amount of ingenuity you might be able to output your pages as single pdfs, then create a new document with the required number of pages, and then place and rotate the individual pdfs in that document. But it would take quite a lot of working out, and Pages wouldn't do that for you.

As for the slight shrinking, I suspect that this is to allow for an empty trim area between the pages. I don't think there is any user control over that.

'Imposition' is the technical term for the process used to achieve precisely what you want to achieve - positioning and often rotating single pages so that they align correctly when printing larger sheets and then folding. If, say, you have a 24-page booklet, then page 1 will face page 24, page 2 will face page 23 etc. It all gets very complicated depending on the size of the larger sheet and the number of pages to be placed on it...

However, if you have a Pages document that you want to output as an A5 booklet, and you know how to create a booklet in Affinity Publisher, why not combine the two?

Print out your A5 sides from Pages as single pdfs, create a blank A5 Affinity Publisher document, add the appropriate number of pages, and place each pdf on its corresponding Affinity page (File - Place in Publisher).

Then output the Affinity Publisher document as a booklet. (I personally think doing the whole thing in the current version of Pages is a bit of a non-starter.)