Someone posted some Nexus recently. It seems to be ongoing again. But I haven't kept up.
Good question. One that might go either way depending on what Nexus is up to these days. I admit I know nothing about Authority.
I don't consider murderers to be superheroes. They're soldiers or metahumans. It is worth arguing whether Ms. Marvel's killings violate her existence as a superhero, since she had no authority to act as a soldier and whether we should all just ignore writer's stupidity as inappropriate to the character.
Nexus is, and has always been, a murderer. He has superpowers and funny tights. He does not patrol, he does not worry about trouble on other people's planets, when people beg him to intervene he refuses, saying, "I don't have to." He is forced by circumstances to kill bad people. He doesn't go out of his way to kill bad people. He doesn't go out of his way to save people.
Superhero books are morality plays. Nexus is a space opera. It's about power and politics and the ripples it makes. It's best, IMHO, to throw out ideas like 'superhero' or 'morality' for this book. (Badger is about mental illness and rude people in Wisconsin) Nexus can be very heavy and a bit of a downer--which is why this unusual lighthearted story is my favorite and the best introduction to this obscure series.