Total HFe of 2n3904 and the 3055 darlington is probably around (or above) 1000, so about (or less) 0.1% error, so it's pretty much below an ADC count and negligible, and you can get an order of magnitude better by calibration. I'd say, do not measure the resistance of your shunt directly, but put a DMM in current mode in series with the battery and use that to calibrate the current.
I don't like the dotted blue lines much. Just the big fat captions are clear enough, and the dotted lines add too much time for maintenance during modifications. It's really a bad idea.
And there are indeed plenty of examples of stabilizing a circuit like this.
Also:
In KiCad V6 you can assign net classes to nets in the schematic. You can also change the color of wires and make them thicker, just by labeling them into a properly set up net class. That looks much better then your coax cables on the output. The setting is in: Schematic Editor / File / Schematic Setup / Project / Net Classes
It's also a bit naughty to discharge your batteries to 2.5V. It's much easier for them if you don't go below 3.2V and it won't matter much for your measurement either.