Hall effect sensor as toggle switch
Minimal circuit could be one chip like an analogue asic but that would cost many, many thousands of dollars. Minimal could of course mean cheap or small or both. Stretching it a bit, minimal could mean low power.

Putting all this to one side, amplify the hall sensor's output, feed that into a suitably referenced analogue comparator. That will produce a high signal when the magnet is close. Feed that into the clock input of a D type flip flop configured as a divide by two and drive the LED, via a resistor from the output.