In a January 19, 2022 Public Health Scotland “COVID-19 & Winter Statistical Report“, figure 13 revealed the unvaccinated having the lowest COVID-19 case rate per 100,000 of all population cohorts, but they warn it should not be an indicator of the vaccines failing to “work.”

a simple comparison of COVID-19 case rates in those who are vaccinated and unvaccinated should not be used to assess how effective a vaccine is in preventing serious health outcomes, because there are a number of differences between the groups, other than the vaccine itself, and these biases mean that you cannot use the rates to determine how well the vaccines work.”