It says in the decription that "a shop produces income based on the total poplation. Makes settlements happier."
but do i personally have to collect money from them? or will it just be put into my caps if they sell anything?
or do i have to send them to other settlements to sell things?
I couldnt find anything on google so im here

They money is deposited in your workbench inventory pool, you have to manually collect it. I don't know how often, haven't checked.