Thanks for the reply!
While evaluating this case, please look at the two attached documents in my original post.
I'm following the attached guide from the ink vendor (I've tried asking them, but they asked me to reach out to you for further assistance) and using sRGB/8-bit and the ICC profile specific to the printer and ink I'm using. I've enclosed the ICC profile as well, so you can try it out for yourself on plain paper (this is for sublimation ink, so it'll probably look different on your regular CMYK printer, but it should still show up differently in the printed output from Photoshop and your application). I'm using a Relative Colourimetric rendering intent (as instructed) and have disabled driver specific color management.
I've used vendor supplied instructions for both applications (and the same rendering intent from the ICC). Both test files look the same in their respective applications on my display.
Is there anything obvious that I should double check that was not mentioned in the attached PDF instructions file that would affect my color work flow?
Affinity Designer 2019.pdf