https://www.science.org/doi/10.1126/science.abi9069
First, note that this wasn't studying in the context of a mask mandate - in the sample villages, masks were distributed, and people were recommended to wear masks when around others. In practice, this brought mask usage up to 42% on average, as compared to 13% in control villages. So, even in this context where the majority of people weren't wearing masks, they still saw an effect in the cloth mask villages. They also saw a larger effect in the surgical mask villages.
Thread from one of the study authors: https://twitter.com/Jabaluck/status/1433036923610742789
It is worth noting that the effect was smaller and the sample size for cloth mask villages smaller than for surgical mask villages, so the confidence is lower than for surgical masks. But with that said, note this from the study author:
> We find a clear and large statistically significant impact on COVID symptoms. We find an imprecise zero for serologically confirmed COVID. The most likely interpretation is that cloth masks reduce COVID, but not as much as surgical masks.
https://twitter.com/Jabaluck/status/1433227618497728514
Now, was the effect relatively small for cloth masks? Yes. But given the results here, plus results we have from mechanistic studies of cloth masks, a reasonable conclusion is something along the lines of: cloth masks have some effect on transmission, albeit a relatively small effect. Other types of masks are better.
Additionally, if the assumption of "the types of masks worn by the vast majority of school children" is correct, then studies showing that mask mandates in schools had an effect on transmission would suggest some efficacy for cloth masks.
Two relatively large-scale observational studies: https://twitter.com/roby_bhatt/status/1502244997764157442
That said, I'm endlessly disappointed that there wasn't a consistent, strong push for people to upgrade from cloth to surgical once supplies of surgical masks were no longer an issue. And mask sizing was also an issue - there are so many masks out there that are oversized for kids. Imagine if the federal government had coordinated with schools across the country to ensure supplies of kid sized surgical masks at every school. Alas.