There's not, though. There's a ton of evidence that vitamin d _correlates_ with COVID outcomes, but this is vitamin d's superpower: it correlates with good outcomes for just about everything, but nearly every time there's a good high quality study, it turns out to not be causative. A bunch of those vitamin d and COVID studies were fraudulent.
Vitamin d levels are an excellent marker of good health and they can help predict outcomes but supplementing vitamin d doesn't improve those outcomes. Regretfully. (Except rickets, of course.)
Yes. There's a ton. Most of it is horribly tainted by correlation effects. Let's consider one of the studies you cited above, which is an observational study from the VA hospitals:
"In the population of US veterans, we show that Vitamin D2 and D3 fills were associated with reductions in COVID-19 infection of 28% and 20%, respectively"
This sounds really awesome, right? Except -- you could also interpret this as "People who are following their doctor's recommendations, going to the pharmacy to fill their prescriptions, and taking them, do better". No kidding - they're probably also taking their other medications and being more generally medically careful!
This is completely consistent with the 99% of vitamin d-related results that show that it correlates with all sorts of positive outcomes.
The high quality interventional studies -- which are actually potentially able to demonstrate causality -- are generally negative. And the larger and better they are, the more likely they are to be negative. One of the largest was the CORONAVIT trial; it was, unfortunately, open-label, but it was large and randomized. (Note that you'd expect the open-label aspect to result in a stronger placebo effect, which .. well, given that they found no benefits, did not occur). https://www.bmj.com/content/378/bmj-2022-071230
The vitamin d & covid horse is pretty dead at this point, which is basically the same as the "vitamin d & x" horse for most values of X other than diseases known to be directly caused by vitamin D deficiency. Which are serious and worthy of treatment. Just don't expect vitamin D to be a miracle cure on the basis of its correlation with everything positive.
There are multiple clinical studies showing that vitamin D supplements can be effective in fighting COVID-19. Some other studies have shown no effect, but overall there seems to be some benefit.
