Microwave ovens are also non ionizing, you can't dismiss the danger just on that alone. Sun radiation is also very dangerous at long exposures, I'm a ginger I would know that. You also don't want to look at it for too long, or at all during a partial eclipse (eye thinks it's darker so iris opens more). Also solar panels don't "attract" radiation, the radiation is there regardless. Actual danger is determined by lot of factors though such as frequency and power. Power alone is not enough nor is frequency alone. Lot of people are afraid of 5G because of the very high frequencies but it actually transmits at less power than 4G.
That said I don't know if the amount OP is getting is actually dangerous or not, it just seems rather high. The fact that it's pulses might make it less dangerous though. Wonder what kind of frequencies or power levels smart meters work at, maybe it's that? I would imagine the source has to be fairly close by. I'm still curious to know if it goes away when turning power off. That would not rule out the power meter since it will still be operating but it would rule out a device inside the house.
Airplanes MIGHT be a source too, ADSB transmits in the 100's of watts I believe in pulses about once a second. Not sure if that is powerful enough to be achieving 34w/m^2 though by the time it spreads out from their altitude. It's a rather unidirectional signal so the power dissipates quickly. it's why they transmit at such high power. Same with FM/AM stations they transmit in the kw range.
What kind of equipment is being used to measure this, is it a portable setup? I would bring it to different locations just to compare values.