You need to add "short run" since these vaccines have not been tested long term. Not to say it is likely at all since other mRNA vaccines have not had long run issues, but to say there is "no evidence" is cheap when long run studies have not been conducted.
Please cite a case where this extraordinary claim has held true. Where a vaccine has caused a side effect not noticeable within the first year.
Globally hundreds of millions have been vaccinated and we've had enough data to get really precise numbers on even the absolute rarest of side effects; which are vanishingly rare and pale in severity and incidence to the disease in the wild.