you can’t change the value because the property isn’t “active” since the operator isn’t running. If all you want to do is set the autosmooth angle for a mesh, why not just pass in the mesh’s property directly rather than doing some kind of round-about method with an operator?
if context.active_object.type =='MESH':
box.prop(context.active_object.data, 'auto_smooth_angle', slider=True)