Defining sensitivity of TOF Mass Spec - Does the detector play a role?
The term sensitivity has been misused in analytical chemistry a lot (even in German scientific literature). Be careful if you read articles especially the older ones. Sensitivity, in a true sense, refers to the slope of the calibration curve. Thankfully IUPAC sorted this out and defined it as "The slope of the calibration curve. If the curve is in fact a 'curve', rather than a straight line, then of course sensitivity will be a function of analyte concentration or amount. If sensitivity is to be a unique performance characteristic, it must depend only on the chemical measurement process, not upon scale factors."

When we wish to refer to the minimum amount that can be detected, it is called the limit of detection (LOD). Hope this clarifies the terminology. Note that sensitivity and limit of detection are related. Higher the sensitivity (= slope of calibration curve), lower the detection limit, provided that noise does not increase.

Coming to the detectors: The limit of detection of all detectors which are based on counting (basically we count ions indirectly in mass spectrometry) is limited by statistics rather not by electronics! This is the fundamental limit put by mother Nature. It is called shot noise. Whenever you count discrete random events, in case of a mass spec. random impinging of ions, there is always an error associated with it which is proportional to square root of N, where N is the number of events.

You can read the article on shot noise (for educational purposes).The Ultimate Limit in Measurements by Instrumental Analysis: An Interesting Account of Schroteffekt and Shot Noise, https://pubs.acs.org/doi/abs/10.1021/acs.jchemed.8b00202