Electret microphone preamp is buzzing , weird noise and cannot find a solution
I find the frequency characteristics of the LM386 very unstable. There is likely to be a high frequency oscillation in the system. This can make a special noise. The problem is caused by 100nF at the output.
If this is really the problem, it can be fixed with a serial RC circuit:

Update:
The circuit is theoretically stable, failures are likely due to the assembly or MLCCs. (The 3V power supply voltage (noise) is also interesting because the operational amplifier gains it as an inverting amplifier, 75/2,2 (34x).)

Lastly I would suggest replacing the capacitor or the resistor to ca. 10 times bigger at the input of LM386 in order to have appropriate lower cutoff frequency and replacing possible MLCC capacitors in signal chain (C1,C4 in this schematic) to film/tantalum capacitors. The film/tantalum construction is free from piezoelectric noise.
A disadvantage of the MLCC can be the piezoelectric nature of the ceramic material. MLCCs can exhibit problematic or disruptive noise (ringing or singing) due to oscillations within the audible range.