One way to avoid the measurement errors introduced by the extraneous lead resistances is to create a Kelvin connection by running separate sense traces to the two-terminal shunt resistor.
In this configuration, large circuit board traces carry current in and out of the current shunt resistor. Much smaller traces that are not in the main current flow but positioned as close as possible to the shunt resistor’s resistance element, pick off the voltage across the shunt resistor and convey that voltage to the AFE. Separating the current carrying terminals from the sensing terminals defines the Kelvin connection.
Very little current flows through the two sense resistances because they are connected to the high impedance inputs of either an amplifier or an ADC, making their resistance much less critical than the resistance values of the leads carrying the high currents in and out of the shunt resistor. Consequently, the voltage drops across the sense resistances are quite small and not a significant source of error for the current measurement.