Congress has the plenary authority to regulate trade with foreign nations, according to the Constitution. It therefore has the authority to approve trade agreements in any fashion it so chooses.
An actual written document which defines a trade relationship with another country is a treaty. Go back and look at the pre-free trade era. Those bilateral trade agreements were approved by a 75% vote in the Senate because they had titles like the US-Japan Trade Treaty.
The first boondoggle was NAFTA. perhaps you are too young to remember the outcry over the vote on that and whether it was legitimate. Clinton and his cohorts rammed it through.
Yet when GW Bush was for pushing Mexican trucking on us, he called NAFTA a treaty which couldn't be violated (paraphrasing but he did use the word "treaty.).