All true except for the smaller viral load, info taken from here:
“Data from COVID-19 tests in the United States, the United Kingdom and Singapore are showing that vaccinated people who become infected with Delta SARS-CoV-2 can carry as much virus in their nose as do unvaccinated people.”
Emerging data suggest that Delta could spread more readily than other coronavirus variants among people vaccinated against COVID-19. But key questions remain.
www.nature.com
The amount of people and the window in which they carry will be much smaller but so far it looks like the amount of the virus carried is the same in the two, when a breakthrough occurs. Something for people to think about if there are worries of spreading it to others in close proximity.