At first it doesn't appear like anything is changing, except the motor magically knows to increase current somehow as you apply load.
This question you ask shows that you're a smart guy, you do deep thinking, and I welcome you to our forum.
The answer to your question is all in the position of the magnet relative to the electrical pole. As load increases a bit, the position of the magnet angle vs the pole slides back a few degrees. As you increase load again, that position of the magnet is further retarded.
With no magnets going past, the stator is still pulses an electromagnetic field, but it all collapses back on itself, and it essentially makes a big heating element with an inline inductor. Put the magnets in the picture, and position them at the correct time to have a positive magnet sweeping by right as a negative field is building at the tip of the pole, and the fields attract to each other as it sweeps past, this attraction, combined with the magnet moving towards the pole. With out the magnet moving, no work is done, and the pole field energy is just distorted by the magnet, it creates a force, but with no change in distance, no work is done, and you still just have an inductively delayed heating element. With the magnet moving, the force of the fields attracting combined with the motion of the magnet gives us the force x distance needed to accomplish the conversion of magnetic fields into work. As you shift that magnet timing towards retarded (by applying load), you cause the field off the pole to grow longer before interacting with the retarded magnet position, this field growing to meet the more retarded magnet is what causes the increase in current. On a sensored motor, you can also increase current directly by advancing hall sensor placement, or doing it electronically. By causing the coils to fire sooner, you can offset the 0 timing KV saturation point, and cause a motor to spin faster, at the cost of additional current (from needing to grow the field larger to hit the more retarded magnet.)
I hope this helps answer your question. If it doesn't, I know there are a bunch of other folks here who can provide a better explanation, or correct any errors I may have made above, as I just worked all night, and it's way past time for me to sleep. lol
Best Wishes, and welcome to Endless Sphere,