That sounds like a bad idea if produce can be freely sold across state lines even when it doesn't meet the standards required in a particular state. It's the right conditions to promote a race to the bottom with the states that have the most lax regulations would be more attractive to food companies with the worst standards (production that meets high standards wouldn't benefit from the extra quality unless they can market that specifically).

Regulations are minimal compared to what most consumers would want and expect.

https://www.ams.usda.gov/rules-regulations/cool

For some things like meat, eggs, and milk: The USDA-inspected processing facility is required to be listed on the package. It is usually not very far-removed from the farm. It's coded, and these days it's usually printed near the sell-by date.

They (the USDA) publish cross-references betwixt the codes and the processing plants.

It's been kind of a pain in the ass when I've looked this stuff up in the past and I wish someone would take it upon themselves to make it easier, but it's do-able.

Depends on the thing. Olive oil, for example, is required to list its country/countries of origin