This is super delayed, but I just finally finished setting this up and it works! I followed this very simple guide using this sensor I got off Amazon. I then used the Statistics integration to get the linear average count the sensor was on and setup an automation when the count exceeds a value for a period of time (still calibrating this but it does work).

This is what I used in ESPHome:

binary_sensor:
- platform: gpio
pin:
number: GPIO14
mode: INPUT_PULLUP
inverted: True
name: "Sound Sensor"
id: sound_sensor
filters:
- delayed_off: 2s

And this is my statistics in my configuration file:

sensor: