How to isolate processor noise
C12 should not connect arbitrarily to a local ground but should connect directly to the microphone ground on J2: -



That's my 1st observation - when you have MICN and MICP pins they need to route side by side to minimize pick-up also. The big problem with where C12 is grounded is that between its ground point (junction of C7 and C5) there could exist several hundred micro-volts of high frequency ground noise due to currents in the ground plane. This is why that chip provides a mic-negative pin - it uses a differential amplifier to amplify the mic signal directly.

There may be other issues like C5 also not connecting directly to the mic ground on J2 also. C7 and C6 also must ground right at the microphone negative point too. Also R4 causes the MICP lead to be very long and clearly, the longer the microphone tracks are, the more they'll pick-up.