The contact algorithm uses a tiny amount of penetration in order to calculate the normal force, so this is the expected behavior and the magnitude of the penetration is negligible in this case.

The hand calculation shows the block as a whole does not slide and this is the result that Ansys provides, most of the contact surface is sticking, only a small portion on the right is sliding.

The reason a small portion is sliding is because the normal force is not uniform, it is higher on the left and lower on the right. Plot the Contact Pressure and you will see that. The applied force on the left face combined with the sticking contact elements creates a moment that causes the left side to press down more than the average pressure and the right side to press down with less than the average pressure.