> putting the laptop under load makes the coil whine go away

Probably be sub-harmonic oscillation. Under light loads the control loop can 'hunt' at a much lower frequency then the loop frequency. Combine that with an unlucky inductor and you get a high pitched whine.

It's an annoying problem because in susceptible designs it'll show up in a small percentage of some but not all production lots.

Take your laptop back.

> Strangely, putting the laptop under load makes the coil whine go away

When the load is low, a switching regulator can enter "discontinuous conduction" mode, where the inductor current periodically drops to zero. This is typically noisier than continuous conduction mode, where current is mostly constant with a small sawtooth ripple.

I fairly recently bought a fanless Shuttle barebone with a modern Intel CPU, that produced unbearable coil whine. It too became silent when kept busy. What solved it was disabling C-states and P-states.