OK, I need some help from members of the community. We recently had to replace a Samsung microwave hood with a new unit. The replacement we chose was a basic Maytag unit. Even though it is a fair unit, the stovetop light underneath was a very dim 15-Watt incandescent vs the 5000K 600 Lumen LEDs on the Samsung unit before. That led me to replace it with a FEIT 40-Watt equivalent LED bulb for appliances. The bulb was a lot brighter but when I used the control panel to turn the light off, it wouldn't go completely off! The bulb stays dimly lit if the light is turned off and only cutting power can turn the light off. I did include a link to the exact lightbulb I used which the store salesman said was good for a microwave hood.

https://www.homedepot.com/p/Feit-Electric-40-Watt-Equivalent-T8-Intermediate-E17-Base-Microwave-Appliance-LED-Light-Bulb-Warm-White-3000K-BP40T8N-LED-HDRP/309489433

It is probably current through some snubber network across the switch element.
And is the residual light really a problem? Because unless it is "leaking" into a bedroom, I would just keep it glowing. It would be problem with CFLs, where it can cause repetitive cold cathode flashing and by that way kill the tube, but with LEDs there is nothing to worry about.

Yeah I think the controller in the unit is expecting the resistance of an incandescent lamp. I've seen this happen with LEDs used on older dimmers as well.

I personally prefer incandescent lamps in microwaves because they can handle the heat much better than LED lamps.

There is usually not much heat in microwaves, otherwise the magnetron will be what would fail very soon.
Plus it does not make that much hours: usual microwave usage 30minutes/day means barely 1000hours in 5 years. So 15 year lifetime means barely 3k hour. Plus the magnetron life is limited to the 2khours ballpark also (and then it is uneconomic).

It sounds like he talking of the surface light on the bottom of the unit, rather than the light inside the microwave itself.

And this does sound like a slight leakage. Are there a night light setting also, most I seen press button once for on and again for dimmer night light then again for off. Do the bulb do anything in the night light setting?