Trouble with TI DRV8825 output
Remember that you are using the IC outside the datasheet suggestions.



Where with a more degraded accuracy, where already between 15% to 25% nominally, you can confuse the controller, considering the relatively low current setting (which seems to be to 1.6A according to the comments). This heavily depends on how is made the layout, as well as any interference with the control IC itself if not even EMI withint the MCU itself, mismatching some control signals. With Atmel parts and huge EMI from motors, this could temporary brick the MCU.

A bit more on your scope screes. Also when the driver is actually output power, it generates a proper signal according to the input squarewave. So what you see (and we don't because the scope time division is too large in your picture) is probably the controller struggling with something. When is not connected to a motor, it is very likely that the output will be simply following the input.

So to finish, to know what actually is going on here, you shall at least: check the mode pins, make the stepper working with a reference within proper values, provide windings characteristics (stepper's datasheet) and, last but not least, a zoom of the oscilloscope capture when the motor is producing the squeaking sound.