Strange noise at peaks of measured sine waves STM32F103
The power line tends to be noisy at the peaks of the voltage waveform because any piece of equipment that contains a non-PFC power supply tends to draw all of its current in narrow pulses only when the rectified voltage exceeds the internal DC voltage on its filter capacitor(s).

The noise is emphasized in your second waveform probably because your load is not a pure resistance, but rather has a capacitive component in which the reactance is lower at high frequencies. This allows the high-frequency noise to drive a proportionally higher current through the load than the line frequency does.

And the noise is proportionally lower in the third waveform probably because your amplifier has a low-pass frequency response that attenuates those components.

If you want to do additional filtering, but you're worried about relative phase shifts, you can feed both the voltage signal and the current signal through identical filters. That way, the phase shifts cancel out for any subsequent calculations.