Nobody authoritative ever said they prevented transmission. Ever. They reduce transmission.

Even if you choose to ignore that, consider: Vaccinated people have shorter recovery times and are less likely to require hospitalization.

That results in a shorter time window for spreading the virus. Furthermore, if you can recover at home you are less likely to spread it to health care workers or other patients.

Vaccines help prevent transmission. They are not 100% effective - the effectiveness depends on the vaccine and variant and study but quite high. That's a long way of saying that they "don't prevent transmission"

In the UK's vaccine surveillance report released today it showed the rate of infection in vaccinated individuals ages 40-79 was significantly higher than unvaccinated.

Edit: Link to report (pdf warning) https://assets.publishing.service.gov.uk/government/uploads/...

The same report says that early results indicate that a single dose of the mRNA vaccines provides a 35-50% reduction in transmissions. Given that the second shot dramatically improves the results, we can assume that number will improve. Those are fuzzy numbers whoever, as it is difficult to measure. The prevention of infections is 55-70%