Is there any evidence for (b)? My understanding is that you are just as likely to get vaccinated and "shed" the virus for just as long, but are less likely to be severely sick.
Your understanding is wrong. Vaccinated and unvaccinated people with symptomatic COVID shed at comparable rates, but vaccinated people are less likely to get symptomatic COVID. The difference wanes considerably if your last shot was > 6 months ago, but is still present.