During the last minute I resoldered the microphone so it aligns perfectly with the whole on the enclosure so I would not have to raise the gain. It is quite sensitive but the software waits for 3 beeps spaced 6 seconds apart. It seems quite reliable.
A cheap microphone capsule salvaged from the junk bin, together the old and ugly LM358 as preamp, feed the audio signal to the STM32F103 (bluepill, bottom dev kit). For this MCU, at 72 MHz, with a DMA capable 12-bit ADC, sampling the audio is a walk in the park. I plan to use the ESP (top) to do the IoT / wifi part of this project.
Ideally you'd use just one MCU, but the ESP has a very slow ADC that is not intended for audio, and though I have a couple SPI codecs (the unconnected Microchip part on the upper breadboard), it was much simpler to do the heavy ADC+processing job on the ARM Cortex chip.
Parts wise... the bluepill is even cheaper than the SPI ADC part!
Most of the mechanic part of this hack will be built around a suitable actuator than can push my dishwasher door open. I ordered one of these, with a 200mm travel and rated at 700N it should be more than capable of opening the door. Speed is not really important.