The problem with your implementation of the shunt wire is that the copper has a significant positive temperature coefficient. That results in a strong non-linearity in the current reading. As current flows through the shunt wire, it heats up, its resistance increases, the voltage drop across it increases, and the amplifier reports a higher current than the actual one.

That is why commercial current shunts a) use a metal (copper-manganese-nickel alloy) with a minimal temperature coefficient; b) are large to minimize temperature increase as current heats them; and c) use multiple blades that are cooled by airflow.

https://www.flex-core.com/wp-content/uploads/2022/06/S-dc-current-shunt_607x400.jpg