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We always appreciate students who put in extra effort to think things through!
One of the tricky things about Bernoulli’s equation (or any similar type of equation) is that they can only be used in particular situations.
In the Wikipedia article, they mention the following: “The principle is only applicable for isentropic flows: so when the effects of irreversible processes (like turbulence) and non-adiabatic processes (e.g. heat radiation) are small and can be neglected.”
In a refrigerator sealed system, the flows do not meet these criteria. There is turbulence, and obviously there is a lot of heat transfer going on.