We might be able to see it better if it was in the original aspect ratio instead of this absurd portrait format.
It's not the coffee, she smiled when she saw Spock's backside. She leaned back to check him out.
Kirk had a cup as well. Sulu was drinking tea on the Excelsior when it got hit by the Praxis wave. I've seen them with drinks in other scenes. The bridge isn't a restricted area for refreshments during duty.
Lifer's juice, as my grandfather called it after his Navy career
She took a drink from a cup that may or may not have been part of the scene.
We might be able to see it better if it was in the original aspect ratio instead of this absurd portrait format.