https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10505422/#ref19

They have shown high efficacy against these endpoints in experimental and observational studies (1–13). Evidence suggests that these vaccines also prevent infection (5, 14–18) and potentially reduce transmission (19–23), albeit with smaller effects against the highly transmissible Omicron variant compared with wildtype severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and earlier variants (24–26).

The exception is Omicron, and evidently isn't a complete exception anyway.

In addition, as this was a conversation originally about vaccine mandates, one of the first mandates in the US was put into effect ~2 months before Omicron was reported in Nov. 2021. So even if no vaccine or booster did anything to stop transmission of Omicron, the mandates were fully justified given the vaccines definitely did reduce transmission and severity of variants prior to that.