The E-field for microwave is AC modulated and gets rectified to look like E field from proximity to line signals near outlet.
The plastic has ~7kV/mm insulation and a dielectric constant ~ 4 with a coaxial conductor in the probe to feed the Darlington which rectifies the E field current in ~<=1uA to ~ few mA pk drawn from the Lithium 3V*2 cells which have inherent current limiting to < 20mA from ESR.
The proximity effect is inverse squared per mm gap from the slot which also acts as an RF antenna (perhaps minimized by geometry).
The oven is also well shielded by the Faraday cage with holes in window shield < 5% of lambda in the door unless extremely dirty on the seal creating a gap with E field leakage.
Microwave ovens were also known to cause EMI on analog cordless phones due the 120 HZ modulation of the magnetron's E Field. Shielded pacemaker technology is no longer threatened by this leakage.
This is a useful tool but the LED energy comes from the battery.
Contrary to myth that microwave ovens heat from the inside out, the polar properties of moisture conduct well with ions (salt) but still has skin effect but since much lower frequency ( by several decades) than conventional thermal ovens which do have a much shallower skin effect.
Microwave has a deeper skin depth in food. Research has shown BBQ is the worst for harmful effects on food due to transformations from burning. Contrary to the myth that microwave cooking is harmful, it is excessive food temperature that is harmful. Just consider the frequency of a 1um thermal wave.
At one time the crystalline structure of some dentist amalgam fillings were once known to act as piezo AM detectors and hearing works with vibration on any bone in the head. So in rare cases, some could hear strong AM radio stations.