I can get a source in a bit. IIRC it was the spike protein that causes some (still unknown) response from the human body. The mRNA vaccine elicit a response from the immune system to reproduce the spike protein.
We have no idea that the spike protein causes long covid. It's much more likely that damage from the viral infection and immune response is at least an equal cause.
Beyond that, the virus causes orders of magnitude more spike protein response, so even if that was true, which it probably isn't, then it is still very unlikely that the vaccine could cause long-covid.
Also, all vaccines introduce spike proteins in the body, not just mRNA vaccines.
It appears to come from a researcher contacted by the site for the article. And it's probably true.
However, there's a few reasons to believe that "long" covid like symptoms wouldn't come from the spike protein alone:
1. As a parent mentioned, you generate a lot fewer proteins w/ the vaccine than the virus
2. IIUC, those proteins are more localized. The soreness with an initial injection is inflammation due to spike protein creation, and that's usually localized to the injection site. The proteins themselves are less likely to travel as widely as the virus.
3. The proteins don't last very long. They're gone after a few days. So long term symptoms wouldn't be due to a continued immune response. They might be due to inflammation that hasn't gone down, I guess, but that seems unlikely to last months.
And again, all of these will be worse with the virus than the vaccine. You'll have more spike proteins, for longer, over a larger part of your body, and also have a virus attacking you in addition to the immune response.
Another thing is that spike protein from the vaccine in the arm has a much tougher time getting to the brain than viruses in the nose/olfactory bulb. That's on top of less spike to begin with.
There aren't actually any virus particles in the mRNA vaccines, so there's no biological mechanism for that to happen.