One concern with observational studies: people who choose vaccination don't behave exactly the same as people who don't. They may assume more risks out of perceived safety. They may also be more likely to test or seek medical care. This is why, at a minimum, you need case control to start to believe the conclusions.
In any case, we have actual case control studies showing mRNA vaccine efficacy against illness and particularly against severe illness from Omicron. They disagree on the amounts, and in some cases the numbers are not thrilling (30%), but there's no studies so far implying no efficacy.
The study we're discussing here concludes its abstract with: "These data support the notion that, provided high neutralization capacity is elicited by vaccination/boosting approaches, reasonable effectiveness against Omicron may be maintained."
I think you could give out 2 doses of a strong laxative and show it statistically protects sick people against covid too. If you take out the weakest, the rest will seem to do better.