Electronic – the source of noise in this current measurement

I like using the closed-loop Hall effect LEM current transducers for this sort of application. They're a lot cheaper than a genuine current probe for a scope (only about $20 or $25), have excellent accuracy and bandwidth from DC up to a couple hundred kHz.

The particular one I've linked has a +/-6A range, but you can put a couple loops through to get +/-3A full scale. Just feed it a reasonably clean +5V and Robert's your uncle.

If you want to make more of a project of it, you can offset the output with differential output between the LEM and a 2.5V reference, or actually subtract it with an op-amp and bipolar supplies, but for most purposes, just adjusting the scope zero will do the trick.

I can not find any circuit that achieves this kind of accuracy.

In practice it is very difficult to get that kind of accuracy (0.01A at 50A is 0.02%) but it isn't necessary. 0.01A resolution is useful at lower currents, and is not difficult to achieve. I did it with a 0.001Ω shunt, precision op amp, and an MCU with 10 bit ADC.

Voltage will sag as the battery discharges, so to get accurate efficiency you need to measure Amps, Volts, rpm and torque simultaneously. However all these readings will have ripple, so they should be averaged over a period long enough to integrate the variations that occur at motor commutation speed.

With all the error sources combined you will be lucky to get better than 1% efficiency measurement accuracy, so don't worry if you can only get a current measurement accuracy of 0.2% (0.1A at 50A).