I was even more curious, and it's pretty hard to search for what information was available on the web in early 2021. So don't judge me, but using ChatGPT is the fastest way I could think to get an idea.
This is what chatGpt thinks was the CDC statement in early 2021:
> In early 2021, the CDC indicated that while COVID-19 vaccines were highly effective at preventing severe illness, the ability of vaccinated individuals to transmit the virus, particularly the delta variant, was still under study. Vaccinated people could carry viral loads similar to unvaccinated individuals, but these would diminish quickly. The CDC differentiated between "breakthrough infections" (vaccinated people testing positive) and "breakthrough disease" (symptomatic cases), noting that both were uncommon. However, exact rates were unclear, leading to updated guidance for vaccinated individuals to be tested and mask up after exposure, especially in high-transmission areas. CDC's program focused on real-world vaccine effectiveness, including against variants and over time
Edit:
I also checked if ChatGPT knows if Fauci ever stated that vaccine would prevent transmission, this is what it had to say:
> Dr. Anthony Fauci initially stated on February 4, 2021, that there was insufficient data to confidently claim that vaccines prevent the transmission of COVID-19. However, by February 17, 2021, he referenced new studies indicating that vaccines might reduce transmission. Fauci cited research showing that vaccinated individuals had significantly reduced viral loads, suggesting a lower likelihood of transmission. Studies supported the idea that the lower the viral load, the lower the chance of virus spread. Fauci highlighted the public health implications, suggesting that vaccination could diminish the outbreak's dynamics
Do with that as you will, it's ChatGPT, not a thorough research into the historical archives, but its better than nothing.