Everyone transmits the virus. The vaccines don’t do much in that regard, though from what I’ve read. They do a good job of preventing severe disease.
The current recommendation is to get a booster because it both reduces the severity of the disease and the chance of either catching a breakthrough infection or another variant[1]/[2].
[1] https://www.cdc.gov/coronavirus/2019-ncov/vaccines/effective...
[2] https://covid.cdc.gov/covid-data-tracker/#rates-by-vaccine-s...
I don’t remember where I read it originally, but the lancet is roughly what I recall. It’s not 100% conclusive, but the data seems to point towards roughly the same transmission rate.
[1] https://mobile.twitter.com/EricTopol/status/1476212140956553...