Microphones are linear. By subtracting their signal-to-noise ratio (in dB SPL) from their sensitivity (in dBV), we obtain the electrical noise floor of the microphone (in dBV). That value can be compared to the equivalent input noise (i.e. noise floor, in dBV) of the amplifier to find out how much noise is contributed by the amplifier. In this case, the amplifier contributes 13 dBA less noise than the microphone.
I provided an alternative answer to my own question after trying to wrap my head around it for some time. Thanks to Mark for improving my question, but I can understand it better like that. I hope it is correct...
The key here is that across most of their range, microphones (or at least all those whose spec sheets were detailed enough for me to check) are linear transducers of sound pressure into voltage. Not only that, but the increase in voltage is 1:1 with the increase in sound pressure. You can see that in linearity graphs in microphone specification sheets. Only above a certain threshold (roughly corresponding to the acoustic overload point), and also below the noise floor, this linear relationship flattens off.
As a consequence, specifying noise floors, equivalent noise (whether it should be called "input noise" for microphones can be a matter of debate, but technically, the microphone inputs voltage into the electrical circuit), signal-to-noise ratio, or sensitivity in dBV or dBA (only at 1 kHz) or dB SPL is equivalent. I am not saying that this is particularly straightforward or helpful, though.
In the end, the signal-to-noise value can be used to obtain electrical noise floors (using the sensitivity value) or acoustic noise floors (using the 94 dB SPL reference value). The latter can easily be compared to the equivalent input noise of amplifiers to answer the question.
Example with the ICS-40720 microphone mentioned above:
The microphone has a signal-to-noise ratio of 70 dB (for SPL, but actually it does not matter). By definition and by that standard, that signal is a 94 dB SPL tone at 1 kHz, thus the acoustic noise floor (which is constant) is 70 dB lower, at 94-70 = 24 dB SPL (in a calibrated audio recording).
This is the same as the equivalent (input) noise figure in the specifications, albeit that it is written in dBV.
The microphone has a sensitivity of -32 dBV. Since it is linear, with a 70 dB signal-to-noise ratio, it would mean that the electrical noise floor would be at -32-70 = -102 dBV.
Turns out, this is actually the figure stated in the specification sheet.
When we compare it against the -115 dBV value for the equivalent input noise of the amplifier, we find that the latter contributes 13 dB less noise than the microphone.