Yes, those two orings fix an oil leak not a coolant leak. However there are two coolant hoses coming/going from the oil cooler that could potentially leak, although I've not heard that they "tend to leak" but I could be wrong? You can see them from underneath if you wiggle some stuff around after removing the splash guard.
OP, sounds like you have two separate issues. Oil on the sway bar and coolant leaking from somewhere. Oil will cling to surfaces if the leak is small enough... I bet your splash guard is coated with oil. Coolant is that pink color and will leave that white crusty residue as it evaporates; that is a good indicator of leak point.
Also note that DIY & associated part you linked for an A6; the S4 does not have an oil cooler like that or in that location. It is entirely different.
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