Are you claiming that you read all the studies linked above and none of them show actual causal determination? We can't really prove anything 100% in biology but the totality of evidence is very strong here.
I recall studies showing significant efficacy even in acute settings, which was slightly unexpected, at least to me.
This is not a study, but it does discuss the biochemistry of vitamin D and the role it plays in the immune system. It is left to the viewer to draw their own conclusions.
COVID-19 and Vitamin D | Association Between Vitamin D Deficiency and COVID-19