How to measure leakage current?
The required insulation test uses high voltage DC where one clamp is put on both the AC inputs and the other probe is put where people can touch (earth wire, metal chassis, low voltage DC components, ...). Because it is DC class-Y capacitors will not be leaking current.

The simplest test to test for AC leakage is to put it on a non-GFCI protected circuit (to avoid trips) and put a clamp meter around live and neutral (but not ground) and set to measure AC. You can frankenstein an extension cord for that purpose. This is how a GFCI works, when that current exceeds the rated value it will trip.

There are more advanced devices that will used high voltage AC instead which will include the effect of the class-Y capacitor.

If that leakage current if because of high frequency noise on the line you can add a common mode choke on the AC input as filter.