A stepper motor is normally characterised by rated current & coil resistance, not voltage. In your case that's 330 mA and 32.6Ω. That'd indeed give you some 250 mA after L298N losses. Note: the L298N does NOT regulate current, at all. That's part of the problem of using it for steppers.
You always need a common ground, and you always have to connect both wires of a power supply to whatever you want to power.