USDA or FDA
On a federal level, my understanding is that edible insects are not regulated by the Food and Safety Inspection Service (FSIS) of the USDA. FSIS is what we typically think of when associated the USDA with food. The FSIS covers meat, poultry and eggs. I didn’t see anything that remotely relates to insects with regard to FSIS responsibilities. Everything else is under FDA regulations. FDA regulates sea food (which is most similar to insects …think shrimp and soft shell crab) and even covers game such as venison. “What does FDA regulate” link: fda.gov/aboutfda/transparency/basics/ucm194879.htm
The USDA may be involved in insect farming through their Animal and Plant Health Inspection Service (APHIS) agency. For example, if you want to import a new species that is not currently in the US, you would need to contact APHIS. It is my understanding that current insect for feed farms don’t really interact with APHIS but I just might be unaware.
State and local regulations is another can of worms. Ideally, federal agencies responsible for food safety and security will provide leadership to state and local authorities.