As explained before, the formula would be a rough estimate of the dBSPL because dBFS is measuring one thing (where the signal stand with respect to full-amplitude) and dBSPL is measuring the actual physical sound pressure.
135dB AOP was an example, if you are using a specific part you should read the datasheet! for MP23DB01HP the datasheet says AOP is 120dBSPL and you should use that number, not the one in the example: dBSPL = dBFS + 120.
The datasheet says that a 94dBSPL signal at 1kHz stays at -24dBFS +/-1dB. You can use this reference point to get the number you are looking for, 118dBSPL+/-1dB at 1kHZ would correspond to 0dBFS. Which again points to dBSPL = dBFS + 118.
RMS is more reliable than an instantaneous measure. So, use the RMS of a data segment to get the same levels that an audio instrument would report (because remember audio applications use RMS).
Finally, for applications that require accuracy you can perform a 1 point calibration: create a stimulus with a precisely known dBSPL level, measure the dBFS level from the microphone and compute the offset to be added to go from one number to the other.
Keep in mind that the frequency response is not flat, signals with same dBSPL but different frequencies will appear to have different dBFS.
Hope you can move forward with your application now. If so, please mark this as solution accepted.