Too many people are trying to overcomplicate things.
I used oil filled radiators for years and never felt the need to make one smart.
Heck a ton now have clocks with multiple on and off options on them. So you can schedule it to turn on and off so you don’t need to touch it.
First thing you need to do is to make sure the “smart outlets” are capable of handling the maximum voltage and amperage of your heater. You don’t want some attempt at making it smart to result in a fire.
Most oil filled radiators have a thermostat on them. Use it and with some tweaking it should work fine without getting alexa involved.
K.I.S.S.
Test at each point in the chain.
Somewhere, something is wrong causing it to drop to 100.