That's the US data which is hopelessly corrupted by politics; the CDC simply hasn't been reporting honest statistics about vaccines from the start.

In the UK where the health authorities break down by age and vaxx status with what seems to be reasonably accurate reporting, the vaccinated per capita rate is ~2x the unvaccinated rate and nobody knows why.

This is incorrect: we don't know the rates, because we don't know the denominators. Published figures use estimated denominators: "because the proportion of unvaccinated people is small and the NIMS population estimates are high, it makes the unvaccinated population appear significantly larger than it is. As a consequence, the Covid case rate per 100,000 unvaccinated people, when calculated using this figure, is suppressed. Just being out by 1 or 2 per cent could change the apparent population of unvaccinated people by 30 per cent." (from https://www.thetimes.co.uk/article/cfaadc98-35ab-11ec-8ef4-8... )

The quote from parent was about transmission.

As every new case is a result of transmission, a difference in the per-capita rate of new cases between vaccinated and unvaccinated people shows an identical difference in the rate of transmission.