The equivalent noise density of the sdp600 is 10^-2 Pa/sqrt(Hz). While the noise density of a typical microphone is 10^-6 Pa/sqrt(Hz). At same 50hz low frequencies. So either you're full of shit and a high quality microphone is x10000 more sensitive than this sdp600 sensor, or I'm not understanding what you're saying.
Any self-respecting microphone will be sensitive to tens of micropascals (the conversion between SPL and Pa is straightforward). The Sensirion device is proud of its ability to operate at 10 Pa.
That being said, most microphones are intended for audio and their amplifiers and readout circuitry are not optimized for very low frequencies. And the physical measurement devices don’t work down to DC. (If they did then the microphone wouldn’t work — the DC pressure is around 1 atm, which is some 12 orders of magnitude above the more quiet sounds the microphone is trying to detect.)
A device sold as a pressure sensor will be intended for use at or near 0 Hz and will work fine.
I assume the actual practical crossover is something like 0.1 - 10 Hz depending on the microphone. There’s an additional practical issue, though: the pressure sensor comes from the factory already calibrated for DC, whereas you may be on your own trying to get physical units out of a microphone much below 20Hz.
If you use a high end microphone intended for professional use with phantom power, you will also be fighting the power circuit and lower frequencies.