Fully remote (home-based), moved NY to NJ thru year

This should be easy and a very common situation, and I THINK I understand it, but I’m not sure, so: for the first half of 2023, I was a fully remote employee for a major national employer, working out of my long-term residence in NYC. In the second half of 2023, I moved to NJ, where I remained m a fully remote employee for the same company, but now working out of my new long-term residence in New Jersey. I updated my my company’s payroll when I moved, so for the 1st half of the year I was officially a NYC employee (home based) and for the 2nd half of the year a NJ employee (home based). I know I need to file 2 state returns, both as a part-year resident of the state. But my two W-2s make no sense. The math doesn’t add up. Can anyone advise on what the W-2s should look like if things were done correctly? Or any other advice from someone who’s been in this situation, which I know there must be a LOT.