When my switch is connected to the same network as my PC, WOL works perfectly. But outside, it doesn't work.

The problem is probably that the WOL function on Moonlight-Switch doesn't send packets to the public IP address, but only to the local one (unlike the Android version).

My current setup: a raspberry that listens to requests arriving on port 9. If this corresponds to a magic packet, it wakes up my computer.
It works perfectly on Android.