A small current is going to flow internally, but nothing else happens. It's quite normal to have solar panels running with zero load in regions with lots of PV

A small current is going to flow internally, but nothing else happens. It's quite normal to have solar panels running with zero load in regions with lots of PV - reason being, that the carriers need to keep their electricity nets stable and have to carefully balance electricity entering and leaving the net. At least in Germany, every PV installation of certain size (> 30kW peak) is mandated to be able to be shutdown remotely by the carrier if you supply electricity for the net and aren't just using it for yourself. (You get paid the same during shutdowns, just like it were running. Otherwise it would be quite damaging and likely reduce adoption of PV) Point being: no, it doesn't hurt the panels and is a regular ocurence.