It would be trivial to do a similar investigation as that performed in the cited study (https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0263069) using simply existing records of #vaxes, #infections (and reaction severity), and measured 25(OH)D levels. That data exists.

Now that I think about it, one wouldn't need a time series but simply reconstruct annual cycles such as that in Fig. 1. The sine curves would simply offset downwards depending on the #vaxes, for example.

Rather than the linear step down depicted, I would expect the step downs to become steeper with each jab as recipients would be less able to clear the spikes due to progressively lower 25(OH)D availability. Recovery in 25(OH)D levels would only occur in summer or if supplements were being taken.