What constituents in soft drinks are the cause their strong pungent smell? Wikipedia and PubChem tells us that $\ce{CO2}$ is odorless in lower concentrations but can have a mildly pungent acidic smell at higher concentrations.

However, there is no pungent smell from chemical reactions such as the combustion of cooking gas, effervescence from carbonate upon the addition of an acid, and the sublimation of a piece of dry ice.

But many soft drinks and soda waters (including Sprite, 7 up, Pepsi, Coca-Cola, and Thums Up) emit, open opening, a strong burning smell that may cause severe irritation to eye and nose. The same burning is experienced during the burping (or belching) that comes out after consuming a glass of such drink

So, I want to know, is this due to $\ce{CO2}$? Maybe the manufacturers pump too much $\ce{CO2}$ into their drinks that it reacts in a different way than $\ce{CO2}$ from LPG-oven flames or carbonate/acid reactions? Or maybe that 'burning effect' is due to some mysterious additive?
Yes, that strong smell is mostly $\ce{CO2}$, possibly with a faint tint of volatile aromatizers from the beverage.

Our sense of smell works in surprisingly non-straightforward ways. Indeed, the smells of the same compound in high and low concentrations are sometimes perceived as quite different, to the point of being totally unrecognizable. A classic example is skatole, which may produce either a pleasant flowery aroma or a fecal stench, depending on the concentration alone. Looks like $\ce{CO2}$ is just a somewhat less extreme example of the same effect.

Air with 5% of $\ce{CO2}$ doesn't smell much of anything (not that it is OK to breathe it for long), which leads most people to conclude that $\ce{CO2}$ is odorless. This is quite wrong. If you try to inhale some pure $\ce{CO2}$ (which I do not recommend or endorse), that's when the smell kicks in. Your breathing just stops instinctively, as if you were trying to inhale water. By that moment, though, some $\ce{CO2}$ reaches your olfactory nerves. I am at a loss of words as to what it feels like. Being slapped across your face with a shovel seems like a moderately adequate approximation. Besides, you feel that familiar refreshing sharp odor of an open Coca-cola bottle.

So no, this is not due to some mysterious additive.