Hi thomaso and everyone who replied!
Thank you for your replies!
Returning to your first message, @thomaso:
Just to be sure: Which preflight profile did you use that did not return an error?
We get the error ("Output Intent not suitable for printing (unknown ICC profile) (V2.4)") with the preflight profile PDFX-ready Sheetfed Offset Classic HQ V1.5.
As I said: The PDF looks fine for printing. So this is mostly a question of complying to our workflow. But we would like to get to the bottom of the question, whether the fault lies with the preflight profile or in the way Affinity Publisher writes ICC profiles into the PDF.