What's the role of milk or yogurt in sponge cake?
A basic sponge does not contain milk, yoghurt or other dairy, neither does his closely related cousin, the pound cake (except for butter, of course).

That said, obviously there are many recipes that use extra ingredients like dairy products. Usually the percentages of the recipes are a bit different from the "base" recipes. There are a few reasons to add dairy (or non-dairy):


Adjusting for fewer eggs
If you get less liquid from the eggs, you need a substitute to prevent a "dry" cake. Keep in mind that the water content may be different when using e.g. apple sauce, sour cream, milk or juice.
Changing flavour
The classic recipes can be a bit "eggy" or bland. Especially with non-dairy liquids like lemon juice or alcohols like rum or whiskey you can completely change the flavour profile. Dairy gently alters, e.g. yoghurt / sourcream gives a slight accidic tinge that cuts the sweetness of the sugar.
Reducing fat in pound cakes
Especially less-watery ingredients like applesauce, mased banana and sourcream can replace part of the butter, cutting calories and adding flavour.