The Second pertains to the right to “keep and bear arms.” It’s open to interpretation whether or not superpowers would qualify as arms.
Oxford/Google:
“arms
/ɑːmz/
noun
plural noun: arms
1.
weapons; armaments.
“arms and ammunition”
h
Similar:
weapons (of war)
weaponry
firearms
guns
ordnance”
I can see this being a contentious legal issue in the courts. Of course the government would fight against recognizing additional rights since they generally fight to centralize power. Those in favor would say that the powers were given to them for a reason and should therefore not be banned, and that they can be used to do good and in self-defense, while those opposed would say that not everyone has superpowers so no one should have more power over another etc. I would be in favor of superpowers even if I didn’t have any because I would be interested to see how that would play out. Superpowers could potentially save us from asteroids and space aliens and so forth, and from bad guys with superpowers. If they made superpowers illegal then only super villains would use their powers and good super people would have their hands tied by the law like in The Incredibles.