Looking at the paper, I don't think these particular magnetite nanoparticles (or any similar small crystal) would be compatible with the Ad26 (J&J/AZ) vaccines, nor the mRNA (P/M) vaccines (at least not as presented in this paper).

These magnetite nanoparticles, due to a slight negative charge on their surface, as well as compatible hydrophobicity attract positively charged slightly hydrophobic polymers (a lot of amine groups and carbon chains) as a sort of coat. This polymeric coating then attracts the negatively charged backbone of the genetic material to be transfected (RNA/DNA). The magnetic nature is then exploited for transfection.

Neither the lipid nanoparticles (mRNA vaccines) nor the adenovirus vaccines have these types of positively charged polymers as listed ingredients, nor would they, as they are self contained with the genetic material inside and employ different methods of transfection. I am not seeing (at least from this paper) how these types of systems would aid directly in delivery of these technologies; unless they aren't what they say they are (like at all).

I'm still trying to rectify the anecdotal evidence of the magnetic effect of the vaccines though. It really makes no sense from the ingredients as listed in any of the vaccines I looked at (J&J/Pfizer/Moderna).