Estimate the ingredients and servings for each restaurant dish, using the menu and 2M recipes. So a "Burger" might have 4oz beef, 1oz american cheese, etc. We have carbon emissions averages for each ingredient from government and industry databases (eg every 1 kg of bananas that you eat generates 0.798 kg of CO2 (based on the production, transportation to store, etc.).
As in whether you walk to pick it up for takeout vs drive to the store to get it? If so then, no.
I wonder whether the best general purpose proxy for the energy intensity and hence emissions is just price. I can’t see how you can get any closer without incredibly specific information about the complete production supply chain, energy mix, etc.
Do you take into account the emissions of going to seek out the food that you've found in the app?