An updated charging script was run, and the result are well within 0.1 mV precision and accuracy!
I also found out that the previous measurements had a little voltage drop (1.5 mV) due to the 1 A current draw, which mostly influenced the scope measurements. Those where uncalibrated better than it previously showed. The question how much they would differ can be answered using the calibration graphs..
I also used channel 2 instead of 1, just to see whether the calibration curve would be different. But as can be seen they're very alike.
Because of a more narrow voltage range (-100 mV .. 1.8 V) the used calibration was done in 50 minutes,.
To conclude: for signals that don't change fast this could be a worthy use of a scope. I think it can even get more precise, it really would have helped if the AWG voltage source had a bigger bipolar buffer capacitor added to it. The battery charging voltage is noticabley more stable.