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.