No, sorry, no and no ! Symmetrical flight means exactly that, symmetrical flight, both wings (more on that later) are at the same speed and same AOA. In a coordinated turn, the yaw is NOT induced by the rudder. If we forget about adverse yaw, a turn is possible only with ailerons to bank, an elevator. Rudder is used ONLY to counteract adverse yaw. Too much or not enough rudder trigger sideslips, but with the proper use of the rudder, there is NO yaw, or if you prefer, the airplane does not turn on the yaw axis, but on both roll and pitch axis, that is what makes a turn. Remember that, for one "action" , a plane has to move on 2 axis, all the time.

Now, to confuse things a bit more, let's talk about induced roll. I said above that in symmetrical flight both wings are at the same speed. Well, depends of the wings, the radius of the turn, and the flight speed, but there is a very well known phenomenon for gliders, where in slow spiral flight (constant turn), because of the huge wingspan, the difference in speed between the external wing and the internal wing is enough to have the EXTERNAL wing seeing a lift increase (due to speed), which tend to roll the sailplane INSIDE the turn, as, in the same time, the adverse yaw is at a maximum, a correct sysmmetrical flight require to have a bit more rudder than normal, and ailerons OUTSIDE (cross control)

Is not trying to understand aerodynamic, fun ?

Bernard