That’s not how it works! The mRNA vaccines cause cells to synthesize the spike protein, but then it is broken down within the cell and peptide fragments of the original spike protein are transported to the surface of cells and linked with a major histocompatability protein. This alerts the immune system to the presence of a foreign substance. The presence of free spike protein in plasma is atypical and very interesting. Some brief searching, including the paper you mention, did not reveal a putative source. I suppose it could even be the inflamed cardiac myocytes, meaning a consequence rather than a cause. I’d be interested to know if the source of the free spike protein is known or suspected.