You’re measurement seems fine to me.
I think the main reason pedalpcb uses schottky here is to minimize the voltage lost from 9V since it’s in a series configuration. Many pedals have a 1n4001 from power to ground. The advantage is that there is no voltage drop in this configuration. The problem is that if you apply reverse power, it fries the diode, and the pedal doesn’t function till you replace it. It’s an easy fix and saves the rest of the circuit, but the schottky in series is great because if you apply reverse power, nothing fries. The tiny 0.2v drop in power is totally worth the better protection, in my opinion.
Diodes (including LEDs) do not just have a perfect single forward voltage for all circumstances, rather the forward voltage changes depending on the current passing through the diode. Here’s a chart from the 1n5817 datasheet. It shows about 0.2v at 100mA, and that’s as low as the chart goes. The gravitation would pull lower than 100mA total through the pedal, so it actually makes sense that you measured a little lower than 0.2V if you measured in circuit. If you measure out of circuit with a DMM, it really depends on what current the DMM is pumping through the diode to measure it. And for sure there can be variation from part to part.T