Agreed that it’s a likely problem.
Here’s a quick teardown of the smart plug meters I’m using (the TP-Link Tapo P115):
No oscilloscope measurements or anything unfortunately, but a comparison to a Kill-a-Watt. Seems to do ok even with a PF<1. It has a shunt resistor and what might be a voltage divider, so it’s probably doing some kind of V-I sampling. But as you say, waveforms can get arbitrarily ugly.