I think correlational studies do have their place. In the world of nutrition literature correlational studies are commonplace because of the large amount of confounders and behavioral aspects to diet. It is difficult to control for exposure to foods, nutrients, etc. as opposed to our ability to control exposure to an intervention in medical research.
This does not however excuse this study for the oversight of cultural differences, exposure rates, healthcare quality, and the large amount of uncertainty that is associated with COVID-19. A little concerning that the sections on limitations and the interpretation explaining why the results didn’t make sense took up most of the paper.