I think there is an error in your hand calculation.
The model does not have a single point of contact, but two points of contact. Take those two points and compute the normal force at each end. Because of the short distance along Y (or X') between the two points and the the distance to the point mass, the reaction force on the bottom is much greater than m.g so maybe the shaft is not sliding but sticking. If the shaft is sticking, there will be no thrust.
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