"began living in NY in 2022"
The state that your wages are from is determined by where you work, not where you live. When exactly did you start working in New York? Unless you worked in New York beginning January 1, you would have some California wages on your W-2.
When exactly did you move to New York? Your income is subject to tax by the state that you live in, no matter where the income is from. Unless you lived in New York starting on January 1, you will have to file part-year resident tax returns in both states.
While you obviously should have promptly notified your employer that you had moved, I would think that your employer knows what company location you are working at, and records your wages accordingly. If you worked in New York, your wages were New York wages, no matter where you lived.
In any case, if your W-2 is incorrect based on where you worked, the best solution is to get a corrected W-2 from your employer. It would be very difficult to try to convince either state that your actual wages in the state are different from what's shown on your W-2.
