What does Stanley do for a living?

Notable that Stanley doesn't seem to have a Southern accent, unless there are speech patterns in New Orleans that I'm not familiar with. Stella doesn't really have one either; maybe from being around Stanley so long?

A few things on that, though...

Stanley's "bro" skills were probably solid. The guy was probably well-loved by other rough-and-tumble types, and that's most of the blue collar types he'll be selling parts to. He was a bit of a "man's man", so he probably could have used a bit of locker room talk and sold some parts.

Just as important is the fact that the play/film are only showing us a moment of crisis in the lives of the characters. Stanley isn't personable during this time period because he loathes Blanche, she loathes him, and so her staying with the Kowalskis is interrupting the flow and groove. If memory serves, there's even a line in the script about Stanley chewing out Blanche for stirring up trouble and making it so Stanley and Stella are fighting. So, we're watching Stanley at his least personable.

I don't want to defend him too much, since I think he's got a lot of repulsive aspects, but it's possible he's a nicer guy (normally) than we see.

Finally, Wikipedia had this note: "No copies of the play drafts mention what Kowalski's line of work is. According to Zurawski, Stanley appears to be an office worker instead of a blue collar worker." Although it also mentions at the top of the article on Stanley that he's a factory parts salesman.

Exactly. And he called it "Désirée"