Student in NC, but resident of CO legally. Worked part-time in NC. How do we answer this question? "Did you make money in North Carolina in 2024, but never live there?"

You can answer yes to that question.  This will generate the NC non-Resident state return which you will need to file to report the income you earned while going to school in NC. 

You will file the NC return first and the the CO return claiming a credit for the taxes paid to NC on your CO return.