Israel is about the highest examined and it is not high enough to know how a control group of vaccinated verse unvaccinated individuals would fare in a place where any other individual was vaccinated or bellow 12.
95% was in a retail lock down environment. In the current environment I am having hundreds of interactions a week with the unvaccinated and if I were unvaccinated would have far fewer, obviously a test run in this environment should achieve less than 95% and may appear that vaccination causes COVID because the economy is running on acceptable risks.
No, the virus spreads as a function of what actions you take and society slows based on what actions you take. If no one is dieing or going to hospital you choose economy and cases go up but if you are highly vaccinated then the consequences are not enough to not open up further and you run with higher numbers of known cases.
A correlation study is irrelevant to how effective vaccination is, just as any other intervention might appear ineffective if it allows systems to remove stricter restrictions with higher societal impact or makes people feel safe enough to participate in additional activities.
Some unvaccinated people in my town feel safe enough to do things because more people are safe and are doing them than in a town with no vaccination and more conservative average behavior, that doesn't mean the vaccine didn't work.