Stephen's still on pretty shaky ground, so he's reinforcing it as best he can.

He caught wind that The Harlot was saying bad things about Olivia, and was intrigued. (Possibly he heard it from Jason, who referred to them back in chapter 2, although not by name.)

Currently Stephen is on the books as Jon's housekeeper, which is why he does things like sweeping and cooking. He'll be looking for more independent employment one of these days, but this arrangement is holding for now.