Did anyone else see what Uhura did there?

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.

we frequently see crew members drinking (often coffee) in scenes in TOS. props were often a typical styrofoam cup painted a bluish-grey.

We might be able to see it better if it was in the original aspect ratio instead of this absurd portrait format.

She took a drink from a cup that may or may not have been part of the scene.

It's not the coffee, she smiled when she saw Spock's backside. She leaned back to check him out.

Everyone is focusing on the drink, but what’s also going on is that Nichelle Nichols is completely aware of where the camera is and then repositioning herself so her face is fully in frame.

The coffee drinking, or the leaning over to be visible in the shot?

Hydration is important! Other crew members should take note. (Surely the consoles are waterproof.)