I have a heat bulb plugged into a smart plug by merosso. Previously used a belkin and thought that was the issue. changed plugs same issues. I hear the plug switch on and off, but bulb stays on. Bulb receptacle is just simple. Like this https://www.amazon.com/Craftmade-K212-O-Keyless-Lamp-Holder/
Heat bulbs usually draw quite a bit of power. Did the load exceed the rating of the plug? If so, you may have welded the contacts on the plug’s relay closed.
Another possibility is a wiring fault, since that fixture isn’t normally connected to a plug-in device.