I'll revisit one aspect. It seems abundantly clear that the indicated currents don't sum to zero (moreso in the unloaded run, but also in the loaded run). That violates Kirchoff's current law, so it cannot happen in real life (absent a ground fault, which is not realistic with such large magnitude over such long duration, let alone dc). So it proves there is a measurement/display error of some type compared to the actual current flowing in the motor.
For clues about potential sources of measurement error: What type of sensor are you using to measure current? Are you clamped onto a cable or a ct secondary? If cable I assume you are clamping on a portion that is not shielded? What kind of data collection device? If someone is familiar with the data collection device maybe there are some relevant settings.
If you really want to have an open mind to the possibility of a bizarre actual dc current (even though it's already ruled out for me), I'll ask the question what is driving this motor? Is it fed from vfd or transformer? Is the motor neutral floating or grounded (it should of course be floating in every case, but again just trying to satisfy your questions which seems to presume the dc could be real).
> buzzing or hamming
I can't dispute that in theory dc current superimposed on the normal current in an ac device could produce buzzing due to changing the magnetic chracteristics (although in such case I'd also expect current distortion and there was no evidence of that even in the unloaded). I chalk it up to a coincidence, there are a lot of things that can cause buzzing. If you want to investigate the noise further, I like the free app spectroid on Android which can display spectrum and “waterfall” or spectrogram. In a noisy environment you can move toward/away from the noise source and see which frequencies are changing (to narrow down which frequency peaks are associated with the noise source).
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(2B)+(2B)' ?