The current spike needs to be there and it doesn't affect the controller.
When PWM is enabled on the TMC4671, it has a duty cycle of 50%. This means it switches the voltage on every coil from GND to V m and reverse. Every motor coil has a capacity to GND - this is only a few pF or even lower, but the hard switching results in a small current spike that's visible.
I=C\\frac{du}{\\differentialD t}
The du/dt can be reduced with output filters, something which is often done for EMI reduction.