Columbia GS is not HES.
Columbia GS students do take the same classes as Columbia’s traditional students take, including “the Core”. Columbia classes are taught by Columbia professors (and a few highly accomplished adjuncts for certain specific classes that require specialized knowledge), and you do take the same classes as the other students at Columbia.
I’ve known several people who attended Columbia GS. They’ve gone on to elite employers, including Google and the big consulting firms. They also get into the elite grad programs, such as Harvard Medical School. You’ll have people with extremely interesting backgrounds in GS with you - Olympic athletes, former Pro football players, actors, former Navy Seals, etc.
Note that the core classes have separate sections for GS students, so you get to know other students in GS. It is the same curriculum/material, taught by the same professors, as the version of that class for “traditional” students.
I can’t speak to St. Lawrence, as I don’t know anyone who attended that uni.