I also have issues with centering when printing from Affinity Publisher with my computer running on Windows 10 Pro.
I've tried the suggestions provided in this thread and some others, included reinstalling the printer driver – which is for a Brother color laser printer (DCP-L8410CDW), by the way.
It's frustrating that nothing works.
In MS Word, I can draw a thin, centered, vertical line on two consecutive pages, and the two lines are aligned perfectly when printing doublesided.
When I try the same with Affinity Publisher (latest version for Windows) the lines are off horizontally by approx. 1 mm, and vertically about 5 mm (!).
I tried to attached the lines test and a triple folded brochure, but both uploads failed (the error message said "-200" something).