Are there? I don't think that the USDA requires it.

In the world of academia, I mean. There's some 2,000 studies published on the effects of RoundUp / glyphosate. It's definitely a different environment from the sort of rigor required of drug trials, but there are still plenty of plant / epidemiology labs paying attention to the topic.

I am not sure how these genes have been introduced, where the copies have been placed, and under what promoters.

But the changes would be documented in the approval request (I would think?). The difference is that crossing two plants has changes that would mean merging billions of bases of DNA, as opposed to a few kilobases. That sort of change in the DNA / expression / metabolic profiles would take decades to fully understand at a detailed level. And the complexity grows even more if that hybrid is then allowed to cross further with itself or either parent. And at any point in the crosses, you might put two enzymes together that form a new metabolite that wasn't seen in either host.

In contrast, if you're introducing 1-2 genes, you can search them for similar targets in human / insect genomes, compare them for similarity to known allergens, and run trials between the modified and unmodified strains. And you can compare how the general technique (siRNA) tends to effect the plant and its eaters across different GMO products.

I'll clarify that I'm also in favor of more testing of chronic toxicity, pre-approval. (I'm in general in favor of regulations ;) ) I just don't think it's quite as risky as one might think from first glance at the regulations.