The bench test of your stator is not relevant as you did it, it is not the right method to solve your problem.
Please note that there are 2 separated circuits on the stator plate:
a) The ignition circuit with 1 pickup (red wire) and feeder coil (green wire)
b) The onboard power supply circuit consisting of several coils, connected in series.
So... you only tested the ignition circuit which has no connection to your power supply.
The problem you have refers to a malfunction of the regulator and/or horn rectifier (in case your Vespa is equipped with it)...
As I beforementioned, if the wiring on your stator plate looks ok and there are no VISIBLE damages to the wiring and the power supply coil arrangement (NOT the ignition circuit), you have to replace the regulator and/or the horn rectifier.
This is a known malfunction, there is no secret behind it since the Vespa PX appeared in the 1980s.
My advice was to inspect the stator plate to easily identify visual defects.