That being said, Nature publishes the highest impact papers, which often turn out to be wrong (or overstated). Still, this isn't some random news source trying to report about science.
0. I realized after commenting here that the journal is Gene Therapy, which is part of the Nature Publishing Group, rather than Nature itself.
By their very nature, big results are more likely to be wrong than small, incremental results. The main reason why Nature is prestigious is because getting published there means the scientific reviewers and editors think your result is really important.
First, the CoVID vaccines have been more extensively studied than most other vaccines by this point.
Second, "long-term effects of vaccines" reveals an unfamiliarity with how vaccines work. Vaccine side-effects show up quickly, within weeks at most. After months or years, the only thing left of the vaccine in your body is the immune system memory it induced.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8828133/
Read the Inactivated mouse brain–derived JE vaccine section.
These reactions seem to be more about mouse brain prions, and there was a rare case of (unproven!!) issues a year out, which were cited during discussions about forced discontinuation.
I can't seem to find that, but anyhow, the > 1 month issues are well accepted.