The trim wheel
sets the speed at which the plane will fly.
Engine power doesn't change the speed; it merely affects the rate of climb or descent.
The fact that the trim wheel can be used to null-out the yoke pitch force is a side effect, but erroneously most PPL training usually plugs this as the sole reason for the trim wheel
The trim mechanism (with the trim tab) is a negative feedback control system which controls the AOA to maintain the set airspeed. It does it by continually adjusting the elevator position.