Assuming what you say is true, then nearly every trade agreement including Nafta and TPP would have to be considered a treaty because they cover a lot more issues than authorization for goods to be traded. They include such things as immigration, access to markets, access to ports and highways and rivers. I'm sure TPP contains all kinds of crap about global warming and limitations on the rights of Americans to drill for oil, mine coal, drive SUV's......
So how can Nafta and TPP not be subject to the treaty clause?
NAFTA is not a treaty, it is a trade agreement and that means it is regulated by the US Congress and not international law.
It has provisions in it that appear treaty-like but they are not legally subject to international law, they are subject to Congressional regulation.
You can’t talk about TPP yet because it’s not public. When it’s public, then that is the time to chime in.