The vaccinated person is far less likely to become infected and therefore less likely to be carrying the viral load.
This is simply false.
When they analyzed the data, the researchers found wide variations in viral load within both vaccinated and unvaccinated groups, but not between them. There was no significant difference in viral load between vaccinated and unvaccinated, or between asymptomatic and symptomatic groups.
The vaccination just prevents severe cases...only that over 90% would have no symptoms anyway, and among the vulnerable group is a certain rates of break through infection. e.g. severe cases.
The vaccination didn't prevent the presence of the virus e.g. the viral load.