How do I know if I was doubly taxed? Am I eligible for work credit in NJ?

I moved from New York to New Jersey in May 2019 but my job didn't change.

I checked my W2 that my state wages (box 16 on W2) for new york are my wages for the full year and my state wages for new jersey only account for about half of my wages. However, my state income tax (box 17 on W2) only has values for New York while it's empty for New Jersey.

I have completed my NY return and I am getting a refund from New York, however, I did pay taxes to New York.

Am I eligible for the work credit given this information? If yes, is the amount that was doubly taxed the amount I earned as a resident of New Jersey (state wages/box 16 on W2) and the tax paid to new york the amount I eventually owed New York (State + local taxes on W2 - refund)?