Most photos don’t convey the actual size of it, because they just focus on the top crossbar, but even so, you can see just how ineffective that “noose” would be. If you search for a photo that shows it in full, you will see that a person could easily stand underneath it. It’s too short, and it is visibly crooked. If you tried to hang someone, it wouldn’t work.
I seriously doubt the people who made it had any connection to the people who stormed the building.