motor movement as in and output
The motorized linear potentiometers (like here on SparkFun) have two potentiometers and a motor. There is no capacitive element. One of the potentiometers is used for the volume control, the other for feedback on the linear position.

You would have to make a controller--maybe with an Arduino--to read the potentiometer to get the position and drive the motor to the desired position. When the motor is off a human can move the slider and the controller would detect that movement via the same potentiometer.

I think this would work well for your application with the assumption that you don't need a lot of force on your rod. If you need more force you'd need a larger linear actuator with feedback.