Electronic – Determining speed of turbocharger via sound

If the sound isn't there you can't capture it. Any microphone can be made as sensitive as you want with amplification. What you are really asking for is good signal to noise ratio, not sensitivity.

Look for small microphones that can be attached directly to the track and otherwise have a low inherent noise floor. For good signal to noise ratio, the analog amplifying circuit becomes important too. You want to carefully filter any power supply going near this circuit, shield it from capacitively picking up other signals, filter out RF to keep the frequencies to the range the electronics can handle as intended, use guard traces, etc. Be extra extra careful in the first amplification stage, which will probably have a voltage gain of around 30. After that, the signal will be higher level and lower impedance, and much less susceptible to noise.

As for the best microphone, I'm not up on which technologies inherently provide the best signal to noise ratio. Look thru some datasheets and possibly build a few with circuits to measure the noise floor.

Look carefully at the frequency spectrum of your expected signal. There might be opportunity to filter out large ranges of what the microphone can pick up, thereby eliminating up front noise with that out of band frequency content.

Put a really big inductor (like 30 mH or so, get a bunch of 5 or 10 mH inductors and start putting them in series one at a time) in parallel with the piezo. And cover your ears. You may need to play around with the frequency and the inductance a bit to get the best oomph. I got a surprisingly loud tone out of a piezo at about 4 kHz on about 4 volts with 30 mH of inductance. I'm sure you can do even better with 12 volts.

The idea is that the piezo's capacitance will resonate with the inductance, producing a much larger sound than you would be able to otherwise.

Actually, for 40 kHz you might want a much smaller inductor, maybe around 5 or 10 mH.