For tea, always made in a teapot, would never stir as no sugar and the milk goes in first so need to stir.
For espresso coffee that I use my own filled pod containers in the dolce gusto there would be no need to stir.
But for a cappuccino, I use a separate milk frother, add that to the cup first and then use my own filled pod containers in the dolce gusto for a shot of espresso coffee to it and do use a teaspoon to make a squishy pattern, so go any way I like. Also the spoon comes in handy at the end to finish of the last of the frothy milk.