[gtsteve]

One of the techniques for a voice assistant to distinguish its own voice from background sound is called a Fourier transform, although I expect that the state of the art in this area also includes some other techniques and research.

If you've used one, you might know that you can easily talk to a smart speaker even when it is playing very loud music, it's the same idea.

This video explains more quite well: https://www.youtube.com/watch?v=spUNpyF58BY