In the schematics for STSPIN220 it shows that a capacitor is needed next to the motor power input.
Can I hook up the driver without one?
I’m using an Arduino uno powered from a computer USB port, and not via an external power supply (if it makes a difference).
You can hook up the STSPIN220 without any decoupling capacitors, but we strongly recommend including appropriate decoupling capacitors close to the board to protect your board and ensure it operates smoothly. It should be fine to power the board from a single 5V power supply by connecting it to both the VMOT and VCC pins, though that will make it even more important to add decoupling capacitors. The GND pins are connected together on the board, so it could be okay to connect just one of them to your power supply (though if you can connect both, that would probably be better).