I think I know what the problem may be.
Although the PDF has an embedded profile it does not have a rendering intent embedded (I believe that InDesign calls this "Output Intent Profile Name")
When Acrobat opens the PDF it expects to see a rendering intent (likely true for many RIPs). If it does not see the rendering intent then it simply ignores the embedded profile and assigns an arbitrary profile and 100K gets rendered as a 4/C rich black.
Depending on how a prepress RIP is set up, you will either correctly get 1 black plate or you will incorrectly get 4 plates (one for each of the colors in the now rich black)
PhotoShop (a simple RIP) opens the Publisher PDF and displays it correctly as a CMYK file with image content only in the K channel.
Affinity Photo, on the other hand, opens the PDF and displays it as a CMYK file with image content in all channels. I.e. Affinity Photo converts the one color (K) PDF into 4/C (rich black)
I can't see a way in Publisher to embed the rendering intent (as can be done in InDesign) which would eliminate the issue.
So this lack of ability to embed the rendering intent will be problematic in production with folks getting unpredictable results. :-(