Only thing that ever did anything was respirator types N95 or better. Everything else was theatre for authoritarian rule.
Discussion
I think it was just to make people feel like they could do something. There’s ample information that cloth masks don’t help. So I find it a little strange to see people wearing them now.
You are right in thinking that their function is psychological in nature , but the idea that it made people feel as though they were helping takes a backseat to it's primary function :
A symbol of compliance.
And conversely , it's absense :
Heresy .