While + present simple or present continuous

Hello, there’s one thing confusing me. In this example (taken from a grammar exercise):

She usually feeds the cat and switches on the TV to watch the news while she has/is having breakfast.

is has or is having correct? Or maybe both sound good? I know that there’s usually implying Present Simple, but on the other hand while seems to refer to an action in progress.

Both are okay, though I suspect the exercise would probably expect the answer to be ‘has’.

She watches the news during the time that she eats breakfast.