RSI

Either your printer driver supports this (aka has a setting for split-printing or Poster printing here), or you have to split/tile up the A3 drawing into two A4 chunks inside Affinity and print those. - Or you print scaled down ~72% on just one A4 page.
 

? Set up your document with 600 dpi first and you are good to go. Or make templates with 600 dpi.

You can also set ad-hoc DPI for rasterized objects at print time, so that objects that need to be pre-rasterized will be rendered at the specified resolution (instead of using the document resolution). Below a vector based job where document DPI is 300dpi is forced to be rasterized first at 1200 dpi, then at 20 dpi, and directed to .ps files, then opened in Photoshop to show the difference:

The file sizes directly show that ad-hoc DPI setting has an effect:

Vectors, shapes and text would typically be rasterized only on printer at the device's maximum resolution and placed images rendered at the specified resolution. 

Designer does not have Pages, it has Artboards. There is an Artboard tool which can create a new Artboard. It is similar to a Page.