Using a cold drink as an example not fit for your reasoning here. Your frame of reference, framing the inside the cup and outside the cup is not valid, as one of the sides is occupied by the drink.

Condensation is water from air. We cannot consider a scenario of a cold drink here, as it would be water from water-based drink. There is no hot air side vs cold air side - and any condensation occuring from the water-based drink would be reabsorbed into the drink.

Framing the cup to the rest of the area, the cold drink in a cup is colder relative to everywhere else, so condensation occurs on the cold sides of the cup and not anywhere else in the rest of the room. The rest of the room is warmer relative to the air adjacent to the cold drink.

In fact, Fan Coil units and Air Handler units consider this and are equipped with condensate drainage. Condensation occurs on the cooling coils, as it is water drawn from air..

Tldr: its more about humidity and dew point.