Hmm, I consider that paper to be pretty weak evidence -- as elsewhere, it shows a hypothesized connection via some intermediaries: they show Vitamin D inhibits inflammatory cytokines, but then presume that this inhibition must therefore help avoid hypercytokinaemia (cytokine storms), despite hypercytokinaemia being an edge case/failure mode of the immune system that is not particularly well-understood.

The paper I shared in my previous post cites work showing that Vitamin D promotes other kinds of inflammatory cytokines.

So, yeah. Vitamin D might reduce the likelihood of a cytokine storm, and circumstantial evidence relying on mechanism-of-action suggests that it does -- but this hasn't been demonstrated conclusively.

What is known, however, and which this paper reiterates, is that if you're deficient in Vitamin D, you're more likely to suffer from respiratory tract infections. Take a supplement!