That style of mug became popular in the 80s, when corporate commuting and cubicle culture exploded, and cars didn't all come standard with cupholders yet. A mug like this could sit on the dash or console with stability, and it was also good for a crowded desk because you couldn't knock it over and spill it.
Which makes it extra funny because they're on a space station not a ship like the other treks. I choose to believe it was foreshadowing that they were going to move the space station to the wormhole and there would be sloshing and turbulence when that happened. It's just solid planning.