How does a hall effect wheel speed sensor work?
But I was curious about how the magnet and the rotor interact to change the field to produce a signal.


This type of sensor is known as a "variable reluctance sensor".

Magnetic fields form loops, and you can think of the path that the field follows as a "magnetic circuit". The circuit includes a permanent magent (equivalent to a battery) and materials with varying amounts of reluctance (equivalent to resistance). Steel has low reluctance, while air has very high reluctance. The field intensity is equivalent to current.

In this case, the circuit includes the magnet, the gear, and the other steel structures that hold them relative to each other. As the toothed gear rotates, it periodically increases and reduces the air gap in the magnetic circuit, which directly decreases and increases, respectively, the field intensity passing through the Hall sensor.