Electrical – How to interface common-ground microphone headset with separate-ground audio device

For starters, you haven't decoupled the microphone power at all. You should split R1 into two resistors (e.g., 4700Ω each), and put a fairly sizable ceramic capacitor (0.1 to 10.0 µF; 1.0 µF gives you a cutoff frequency of 34 Hz) from the middle junction to ground. This is the most direct path by which power supply noise can get into the audio input chain.

The next way would be if the opamp has poor PSRR, in which case, you should decouple its supply with a dedicated resistor and capacitor. The problem here is that you don't have a lot of headroom to work with, which will limit the size of the resistor you can use (voltage drop based on the average current that the opamp requires), which in turn will require a relatively large capacitor in order to get a low cutoff frequency.

through 4-wires cable splitting at ~1 mt from the connector.

One meter of thin cable has indeed some resistance. But you can eliminate this almost altogether by splitting close to the connector, which makes the circuit look like this:

^{simulate this circuit – Schematic created using CircuitLab}

Note: R1-R5 are the resistances of the copper cables.

In other words, a shorter common wire will have less internal resistance and thus less crosstalk.