I'm not sure about sharing a font file open to public here (copyright issues). (any idea?)
But the fonts are embedded into the PDF (screenshot 1), what Aiffinity seems to ignore. When I open the PDF in Affinity Photo, I get only asked for GoudyOldStyleT – which in fact isn't used in the original InDesign file. But already in the PDF, too, so it's not Affinity's fault here. Weird.
However I tried to narrow it down. The missing Goudy font is not the problem. IMO.
I tested other PS (Type 1) fonts. In general, Affinity Photo opens PDF with Umlauts in Type 1 fonts properly.
Then I took just one text frame from my original document, using FM Interstate font only, and put it into a completely new document. Export to PDF, fonts embedded. Affinity didn't ask me for font replacement, but doesn't read the Umlauts properly either (screenshot 2). So my guess it that the problem has to do with the particular font family FM Interstate, since other Type 1 fonts work properly.