You seem to be conflating the vaccine having efficacy against infection and whether a vaccinated individual who still catches COVID-19 (since protection against infection is obviously not 100%) can transmit it. The efficacy against original COVID-19 strain infection was high (91.3% for the Pfizer vaccine).
Your first link speaks to the situation of a breakthrough infection being further transmitted. Since it wasn't clear HOW MUCH it curbed infection (under non-ideal/trial conditions), quarantines and caution were reasonable.
Here's a chart that showed the original test results across a number of vaccines. The efficacy vs infection dropped quite a bit with variants though the efficacy vs severe disease holds up better:
https://jbiomedsci.biomedcentral.com/articles/10.1186/s12929...