This is somewhat well covered in prior research, in so far as the information required is available. Here are some recent evaluations of the carbon footprint of modern models:

https://arxiv.org/abs/1906.02243 (cited in the above paper)

> The U.S. Environmental Protection Agency (EPA) provides average CO2 produced (in pounds per kilowatt-hour) for power consumed in the U.S. (EPA, 2018), which we use to convert power to estimated CO2 emissions:

> CO2e = 0.954 pt

> This conversion takes into account the relative proportions of different energy sources (primarily natural gas, coal, nuclear and renewable) consumed to produce energy in the United States.

(Other countries are also included in the paper.)

https://arxiv.org/abs/2104.10350

The authors note that in many cases accurately estimating the carbon footprint is difficult because the information required is not publicly or readily available. However, they do provide some additional data, improved calculations, as well as motivations beyond CO2 reduction.