Actually, I take that back, I think that both examples are side effects. Your output is a side effect of the Omega function, because it is not just a dependent on what Omega does on different inputs, it is also dependent on what Omega does in counterfactual universes.

I am confused by this issue, and I am not trying to present a coherent solution as much as I am trying to stimulate discussion on thinking outside of the input-output model of decision theory.