Your question states that you moved to North Carolina in January of 21. If your facts meet the NC State definition of residency beginning at that point, then all of your income from the point of that date is taxed by North Carolina regardless of where it was made. On the flip side, any California withholdings from that same period should be fully refunded to you: California does not tax employees working remotely from out-of-state on behalf of a California-located employer.
If you still hadn't officially "moved" by state statute, you may be able to claim that your part-year residency in North Carolina began later in the year and you were still CA residents until that time. In that situation, CA taxes the income you made prior to your move, because the resident state is allowed to tax all of your income no matter where it was made.
The circumstances you state strongly suggest you should use the first treatment, but we don't have all of your facts and circumstances. You do. And this can mix with state statutes on what constitutes "residency" for tax purposes: something that varies from state to state. But this much is certain: you were a California resident until you became a North Carolina resident. What date was that? Claim the correct date as provided in the residency laws of North Carolina.
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