You can absolutely adjust the current for a stepper motor. Lower currents use less power, but have less torque, leading to an increased chance of missed steps. In a system like this, the motor torque becomes a linear force to move a belt — and the force required to move the belt depends on if a piece is moving with it, and which piece. It’s perfectly reasonable to bump up motor current when moving a piece, and bump it down when moving just the belt to grab the next piece.
> Steppers use the same current whether moving or stationary.
You can turn off the power when you're not moving it, assuming it doesn't need to hold anything in its place (like in this application).
E.g. https://www.allegromicro.com/-/media/files/datasheets/a5984-... describes how its current control in general works for this stepper motor driver in page 9 (certainly not using the same current always) and in page 12 how to use its ENABLE signal to control FETs and SLEEP to further reduce power usage.