From your link:
“The legislative process for free trade agreements was established in Section 151 of the Trade Act of 1974.”
And from your Heritage paper:
“Somewhat more troublesome is the modern practice of so-called congressionalexecutive agreements, by which some international agreements have been made by the President and approved (either in advance or after the fact) by a simple majority of both houses of Congress, rather than two-thirds of the Senate. Many of these agreements deal particularly with trade-related matters, which Congress has clear constitutional authority to regulate. Congressionalexecutive agreements, at least with respect to trade matters, are now well established, and recent court challenges have been unsuccessful. Made in the USA Foundation v. United States (2001). “
You’re trying to support Session’s assertions but it won’t hold up as case law does not support trade agreements as treaties.