How Power measured by Meters is affected by Harmonics?
There are electromagnetic energy meters with rotating aluminum discs and electronic energy meters, but I have never heard of an "electro-static" energy meter.

Electromagnetic energy meters measure real power and ignore harmonics because they measure power as the speed of a small motor that has a synchronous speed that is proportional to frequency. In effect, they can not measure harmonic volt-amperes because they can not tour at more than one speed at a time. There are torques developed due to harmonics, but some tend to drive the disc in the same direction as the fundamental and some in the opposite direction. The torques and counter-torques do not match, but they apparently don't interfere with the proportionality between speed and real power.

Electronic energy meters work by calculating instantaneous power at short sampling intervals. They multiply instantaneous voltage by instantaneous current. The result is integrated to calculate average power. If the voltage waveform is sinusoidal, no real power is transmitted and the result of the calculation is the fundamental power. If the voltage waveform is distorted, there is real power transmitted at both the fundamental and the harmonic frequencies and that is correctly included in the calculation.

If the objective is to calculate the power separately for each harmonic, the individual harmonic voltages need to be determined. I believe that fourier transform methods can do that.

I hope that provides a satisfactory intuitive explanation. Perhaps someone else can provide a rigorous explanation.