I actually have the correct answer. They have 3 versions in their archives
They have the literal 1991 Special Edition LD release: https://lccn.loc.gov/96517622
A 35mm copy of the laserdisc version: https://lccn.loc.gov/92509477
The abomination that is the 1982 version: https://lccn.loc.gov/91482431
So basically here we have a version that is closer to the original than what the Library of Congress has. It’s confirmed.
Based on the notes of the 35mm link they are at least aware that parts of the original are deleted and what they have isn’t original. Why that doesn’t bother them is shocking considering their policy on Star Wars.