No, the gold splatters is not vector and I know it. That isn't the problem. The missing linked files aren't missing, I just forget to upload them to the drive, where you found the file.
I tried every pdf output, but none of them worked. I made the logo in Designer and the business card in Publisher. The logo looks like as a vector, but when I saved it, then it rasterized. In the beginning, I didn't think that the brush strokes are the problem. Now I seached more and I found the post, what you mentioned:
"Currently Affinity Designer doesn't support "pure" vector brushes and by this i mean brushes composed by vector objects rather than images. ... We do have plans to improve the vector brush engine to include/support true vector based brushes later."