Binge eating isn't about appetite.

While I agree that it isn't surprising the same meds will help with both, it isn't because the glp drugs change appetite. They shift a lot of stuff in the body, and that includes hormonal interactions. That's where the effect is probably coming from, not the appetite/satiety factor

Not having an appetite hasn't stopped me from binge eating in the past. I'm guessing it's more about this part: "... potentially influencing brain processes of reward and impulse control".