What could be the reasons for a stepper motor stuttering with an A4988 driver?
After many days, I have finally tracked down the causes of the issues.

Software

I misunderstood the purpose of Pull Up/Pull Down resistors within the MCU. I thought floating pins (which the STEP pin on the A4988 driver is) had to be pulled up/down. However when changing the output of this pin, there is no need to use Pull Up/Pull Down resistors, simply setting the output is sufficient.
You can see the question and answer posted about my software here.

Power source

Initially, I decided to use a 12V to 5V DC step down converter. This appeared to work at first (in the sense it was providing the correct voltage to the driver), but when I took readings of the voltage between the output pin on the Nucleo-144 and the GND pin on the driver, it gave fixed readings (there was no evidence of the output of the pin changing, despite the program running). Weirdly though, when taking a voltage reading between the GND pin on the Nucleo-144 board and the output pin instead, the voltage changed in the way it had been written to in the software. So, I connected up the 5V and GND pins on the Nucleo-144 to the driver power pins. When taking the reading between the GND pin on the driver and the output pin of the Nucleo-144, it was clear that this voltage issue had now been fixed.

Setting the potentiometer

Having done a bit of searching around into motor stuttering, I came across this post on an arduino forum. In short, it mentions how the potentiometer being too high or too low can cause motor stuttering. I adjusted this, with the power running, until the motor was stepping nicely (without taking any backwards steps).