I think it will have no material impact on her career. It may very well be causing her enormous personal and emotional distress, though, and I think that's important.
The reason I think it will have no material impact on her career is that she is beloved both as an extremely talented actress but also as someone who comes across as a very normal, real, and funny person. The most common reaction to the leak is outrage at the leaker and sympathy for her plight.
So, how should she react to it? First, through a dignified and firm statement released through her publicist. That's been done. Second, of course she's going to be asked about it in an interview context – so she should be ready with one of her classic funny lines.
She has nothing to be ashamed of here.