Any idea how many people we need to vaccinate before we get good info on the impact on transmission?
To get data about the likelihood of transmission, you'll have to have a working track and trace. You don't only need data about the vaccinated person, but also about all their contacts. And you also need to have a low transmission ratenin the first place, otherwise there are too many possibilities of transmissive contacts.
The other approach would possibly be the 'big picture' ('big data') approach, where you compare r-rates between a group of mostly vaccinated people and mostly un-vaccinated people. But with all the different levels of social restrictions in place, I'm not sure if they could find two comperable groups. And also, the rate of transmission in the vaccinated group would likely be very small, so it would take a long time to get that data.
What they have done in the recent studies is tested if someone who has been vaccinated can still carry enough virus particles in their upper airways to be infectious (while not getting ill themselves), and they a found a few people that had that. However I think here is where the general amount of cases comes into it - if there are less infectious people, the virus load is lower, and less people will carry it around with them, which means less infectious people, and so on...