Stepper motor causes voltage drop when running
Whenever the load regulates the voltage, we can define it in terms of % voltage error which then can be used to compute the source impedance ratio to the load.  This is called % Load Regulation Error.
For a battery this source impedance is the total of effective series resistances or ESR.
The motor coil is 2.5 Ω ±10% per phase thus 4A worst case with a drop of 0.6V/5.2V=11.5% which is rather high.
means 600mV/4A = 150 mOhm ESR so you expect the load to be 150 mΩ / 11.5%= 1.3 Ω  (1.25 +5%)
The drivers have an RdsOn of  280mΩ &amp; HS 290mΩ LS.  These are all expected losses are normal for you what.  Minor improvements can be done with twisted  pair (UTP or STP) wiring for everything to reduce crosstalk and low ESR caps. Otherwise the batteries are showing their age or quality.  This is the challenge with low voltage motors to get low losses for each circuit as the currents demand heavier gauge and shorter wire or upgrade the power supply.