The portion of the study posted does not suggest that someone with COVID benefits from vitamin D supplements. It refers to those with good Vitamin D levels beforehand, and Vitamin D is one of those that takes a long time to rise in the system, generally well beyond the scope of a COVID infection.
The initial studies I read a couple of years ago predominantly showed better outcomes if Vitamin D levels were not low, with high fatality rates if levels were <16ng. This meta study suggests that it also helps in not catching COVID to begin with.
By and large, it appears that Vitamin D is very good as a prophylactic in getting your base D levels up, but does not help much as a treatment.
Vitamin D is one of those that takes a long time to rise in the system
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A person with deficiency can have an optimal level in days. A few people increase their levels slowly. Drinking beer helps them increase their levels faster.
There is also a type of vitamin d that is already converted to the blood form before giving it to the person. The injection increases the level to the maximum possible for a dose once the injection ends.