Source: https://www.thelancet.com/journals/laninf/article/PIIS1473-3...
* Peak viral load, GIVEN catching it?
* Duration of peak viral load, GIVEN catching it?
* Severe disease, GIVEN catching it?
* Hospital stay, GIVEN catching it?
* Death, GIVEN catching it?
There are many relevant parameters that the vaccines might affect. And the vaccinated people have a few parameters: number of shots, time since last shot, age, etc. People seem to focus on one or two of these questions at a time.
From your link, actually, related to duration:
"Fully vaccinated individuals with delta variant infection had a faster (posterior probability >0·84) mean rate of viral load decline (0·95 log10 copies per mL per day) than did unvaccinated individuals with pre-alpha (0·69), alpha (0·82), or delta (0·79) variant infections."
Clearly it's not going to stop transmission, but it could slow it down. People on both sides of this issue seem to undervalue partial measures and tradeoffs.