Early in the Covid pandemic research found that infected patients with optimal vitamin D levels were less affected by the virus. https://scitechdaily.com/study-finds-vitamin-d3-important-fo...
https://www.frontiersin.org/articles/10.3389/fimmu.2022.7904...
The results are hedged with might and could and they suggest further study would be a good thing, and it notes that their observations might be related to another thing that might be interesting in COVID patients.
There's no concrete tie in to COVID there and is really just commentary on 12 weeks of study that might lead somewhere that could be COVID related.
It literally doesn't even directly look at COVID, that connection is vague, indirect and couched in terms of "deserves a look".
Papers that address vaccine safety will look at large populations (and provide numbers and time frames) and provide hard numbers on various classes of outcomes.