oil in resivior why? on 2000 Saturn LW2

oil is low on dip stick

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2 answers
If oil is getting in your coolant, then coolant may be getting in your oil. Check your oil dipstick and oil fill cap. Does it have a brown milkshake substance on it? Does the oil seem to be a funny color or thin? These liquids are separated in your engine by gaskets such as your head or intake gasket. If they are going bad then it is possible for 1 or both fluids to contaminate another system.
I have the 2000 LW2 V6.

I have the same (similar) problem right after replacing water pump.

It was leaky and missing coolant, and finally the water pump just seized.
After replacing the water pump myself, I noticed an oily stuff in the
coolant reservoir, paid no attention for a month and now the coolant became very
foamy and definitely there is oil in it. Check engine oil level, surely it is
about one and a half quarter lower!

But my engine oil does not has water in it; look and smell the same.

After a brief research online, someone suggested that, since
no water in oil, it is most likely the oil cooler, which is located on
top of the engine block, right under the air intake manifolds.

I have not started to fix it yet and thus cannot confirm if it is true!
Anyone else has done such a repair?