Okay, I think I've got it!
The main issue was that, although I have double checked if the laptop power supply is galvanically isolated, somehow I got different results with the laptop power supply plugged in and out. The ones I got with the laptop power supply off were closer to reality.
Also, I thought that the reference voltage or the constant to calibrate (turn) the samples into voltage is V_samples x 5/1023, but actually 5V is not the correct value in my case — it's close to 4.5V.
I also measured the 3.3 pin that is on the board, and it was 3.69V or something. The 5 volt (dedicated) pin was in the range of 4.6V, not 5V. When I looked at the discrets ADC is taking, I did see some samples in the range of 866 as a peak value, and was wondering how that was possible. If 1023 corresponds to 5V, then 866 should correspond to 4.23V-something that was never delivered to this board, at least mathematically.
Adjusting the reference voltage and the laptop powered only by the battery helped
The reason for that could be that the nano board is not the orginal one.