I suspect people have a question in their minds for months ("Will the upcoming vaccines prevent a vaccinated person from carrying and spreading the virus?"), and whatever is the first credible reply to that question, they cement it in their understanding ("you may still spread covid if you're vaccinated").

Now we have far more real world data and it appears that even if a vaccinated person is carrying an asymptomatic infection that they shed very little virus. This is not a certainty, but things are leaning that way.

But people can't replace the old "fact" they knew with the new "fact".

Not proven, but looking increasingly likely. From your own link to the CDC, "A growing body of evidence indicates that people fully vaccinated with an mRNA vaccine (Pfizer-BioNTech and Moderna) are less likely to have asymptomatic infection or to transmit SARS-CoV-2 to others."

I'm not sure why people keep saying this. The original studies did not study if the vaccine prevents spread, that is true. I'm not certain myself, but I believe that studies done based on COVID spread in countries where vaccination rates are high (at least Israel) point to the direction that it prevents spread as well. Are these not valid data points?

There was also the Seychelles data point which had the highest vaccinated rate and then had a large outbreak after.

The outbreak was mostly in unvaccinated people, and there was no background of prior infections (they never had a first wave).

Besides, studies on healthcare workers, who are tested regularly, showed a clear reduction in transmission.

Which vaccine did they use? The CDC says the strongest evidence for preventing spread is for the mRNA vaccines.

The vaccine produced by China's Sinopharm company:

https://duckduckgo.com/?q=sinopharm+seychelles&t=fpas&ia=web

Not entirely accurate. From the top article in your search:

"Among the vaccinated population that has had two doses, 57 percent was given Sinopharm, while 43 percent was given AstraZeneca."

I thought I read that it was proven to significantly reduce the likelihood of infection as well as completely eliminate the risk of hospitalization if you do get infected. Admittedly, the media coverage was abysmal (everyone was just quoting “90% effective” without clarifying “effective at what?”).