A linear Hall sensor can be used to measure magnetic field strength along 1 axis of the sensor. But you might want to learn more about magnetic fields and induction before messing about.
A changing/moving field will have different effect on the vessel and be affected differently by the vessel. On more thinking, I'm not sure how you would align the thing to get any complete idea of what's getting through but the idea is just see what data you get with and without the pot in the way.
Maybe it'd be best to just try and run a lab spinner with a stainless steel cooking pot instead of a beaker on the platform and see if the magnet spins? And maybe check how hot the pot gets. But first, ask an experienced lab person if it's a good or bad idea to put metal on the platform. Thin stainless with high current flowing through it... maybe you won't need the heater if it will work at all. Notice in the video, that's a glass plate the egg spins on.
Could you use immersion heater(s)? If so, could you use a plastic vessel?
Or make a kind of stick blender for the stirrer?
There's so many unknowns about this you may not know just how it will behave until you try. I'd go with turning the stirrer from above if I was in a rush. Much less to ponder there.