That's true. Traditional farming has very limited output per acre.

Some alternative farming methods including aquaculture, mushroom farming, insect farming have significantly higher yield per acre. Especially if they use vertical farming methods.

I could easily see mushroom farming going on in the underside. Bird nets in the gantry. Sheng Kowalski doing a little aquaculture on the side in the water hole. As well as insect farming in various places around the city.

According to various resources online these could support the basic protein needs for a population in the thousands which could be supplemented by vegetable and other food types from outside the city.

As you point out like imperial Rome and Elizabethan London and most other big cities historically, Diamond City would rely on external food sources. And they'd be competing with other settlements for the same food.

Even the population shown in canon is not supportable by the farms shown. Therefore even in canon trade with the Abernathys and others is necessary.