According to a study by Victor Chernozhukov, Hiro Kasahara, and Paul Schrimpf of MIT, mask mandates for employees have directly reduced Covid-19 transmissions.
Based on data from April through June, it has been observed that the US states with mask mandates in place for employees tend to have lower overall cases and death rates than states without any mask mandates. The study says that the effect of wearing masks is direct, essentially confirming that wearing a mask lowers the transmission risk.
In addition to these findings, the study notes that if we had kept non-essential businesses open, we could have seen a 15% increase in overall cases and deaths, and without stay at home orders, there could have been an 80% increase in total cases by the start of June. This implies that 0.5–3.4 million more Americans could have been infected without stay-at-home orders.
These findings suggest that these containment policies have greatly reduced the Covid-19 growth rates in the United States. You can read the full study here.