Well I am not an expert, initially the power came from 3.3V of Orange Pi that were powered by an AC adapter.
I then try to use a voltage converter to get 3V from USB (of the soundcard) with no luck,
I then also try a “Wemos battery shield” that provide 5V and/or 3V from a 18650 battery (only powered by battery)
The last try and the only “successful” was with the two AA batteries in series to provide 3V.
That lets me think that 50Hz may not be the (only/main) source of the noise.
The good news is that the circuit on ADMP401 breakout seems not very power hungry, it is running from more than 3 weeks.