My worry would be that you'd have to do some diagnostics on the audio to determine the actual sound. The loudest noise my washer makes is the spin/rinse cycle, which is right before the sound it makes when it's done. You can't just key off of "loud noise" and I don't know how hard setting up to listen to specific frequencies for alerting is.
> You can't just key off of "loud noise" and I don't know how hard setting up to listen to specific frequencies for alerting is.
Fast fourier transform on the audio would give you volume for each frequency range. That probably requires some DIY hardware & programming.
But a power metering plug would be a cheap off-the-shelf solution. Find the ones pre-flashed with ESPhome for ~$15-20, find thresholds for ON/OFF with a bit of trial and error, and you're done.