How much of these cities' carbon emissions are caused by the manufacturing of products for people living in the countryside? Big factories tend to be in or near big cities where there is a workforce to support them.

As an example here in Germany, the city of Wolfsburg has the original Volkswagen plant. It's so big, it's literally called "car city" ("Autostadt"). They certainly don't make cars just for Wolfsburg, or just for city dwellers.

I'm not sure you're comparing like-for-like. A large number of the people living outside cities are subsistence farmers in developing countries and have unsurprisingly low carbon footprints. There is significant lifestyle inflation as the rural populace move to cities.

While we’re on the topic of carbon emissions what’s the footprint of the post office? Driving around junk, the printing of which burns carbon, with combustion engines, most of which is thrown away immediately.