It does sound like a relay but not sure what switch PS uses. I tried setting the trigger a little higher but got same result. Can you expand on safety concerns? Not sure what you mean by inconclusive PE connections?
Most powerstations allow operation of class-I appliances, that need a PE-connection to be safely operated. Powerstations are sometimes grounded by a mains connection or ground wire, but sometimes they are not.
More over that, the power from the mains grid has one neutral and one live wire. The neutral is also near earth-potential. In case of a powerstation you don't have this connection, you should assume that both wires are live, but they may be galvanically isolated.
The Zoyi-scope probably uses probes with a ground clip. Usually a scope only is safe if you safely can touch the ground level of the probe.
In the setup of a battery-powered scope like the Zoyi with a battery powered power station you have combined everything that makes a safety concern.
I don't say don't do you experiments - but please do it together with someone who has experience. Take great care to not touch anything conductive - but to be honest if "take great care to not touch anything conductive" is the whole safety consideration, then it´s too dangerous.