So I think you don't need to measure the capacitance per se. Instead you use the capacitances to make a series of (AC) voltage dividers. The lines that are indi

So I think you don't need to measure the capacitance per se. Instead you use the capacitances to make a series of (AC) voltage dividers. The lines that are individually broken out (call these the vernier lines) will have different degrees of coupling to the sense node, depending on the caliper position. Assume the capacitance of the sense node is fixed. The controller pulses each vernier line in sequence and measures the sense node in turn. The higher the capacitance of a given vernier line, the more voltage will couple across to the sense node. The highest pulse tells the controller which vernier position it's in, so the absolute voltage levels don't matter, conceptually speaking. As for the distance between plates, a caliper ought to be made to a high degree of repeatability. PCB thickness not so much though, probably 10%? To first order capacitance goes as ~1/d. But again, the measurement is relative, not absolute. As long as all the capacitances are affected by the same distance factor, the scheme still works. Anyway, that's an informed guess based upon those scope shots.