I have 2 floor lamps in my living room. Lamp 1 is on a switched outlet. Lamp 2 is across the room. I would like to be able to switch on both lamps at the same time without having to rewire outlets (expensive) or stretch an extension cord (dangerous). So an inline device that would sense power on Lamp1 and switch on Lamp 2.
You must do your shopping for smart home devices. Specific product recommendations are off-topic on this Stack Exchange (although I did give a specific example in a comment).
What you’re looking for tho is a wall switch that acts as a controller for one lamp, and a plug in module for lamp 2. You don’t need to sense voltage at all, you just need a smart switch that will turn on another device as well as itself. In some cases you may or may not need a particular systems hub. I would also watch out for systems where internet connection is required for the setup to operate correctly.