First, the withholding (box 17) should be what was actually withheld, regardless of whether it was right or wrong. It can't change unless the employer refunds it to you. The state wages (box 16) would be what the company considers to be wages subject to state tax. If it is not accurate, you can fix it on your tax return, but you may get an assessment from the state and need to have an explanation ready of the change.
Second, and possibly more important, did you continue to work for the same employer? If you are working for a NY employer out of state for your own convenience, NY taxes all your income from that employer. If you are working out of state for the employer's convenience, then you are only taxed on income earned while physically living or working in NY.
For example, suppose your employer has an office available for you in NY, but you ask for permission to work remotely for your own reasons. You are subject to NY taxes on all your wages from the NY employer. On the other hand, suppose you are a sales rep for the western states, and the company wants you to live close to your customers. You are working remotely for the employer's convenience, and your wages are not subject to state income tax.
Also note, that even if you are working remotely for your own convenience, your wages are not taxable in NY as long as you never set foot in the state during the tax year. That does not apply to 2023 since you started the year there. But if you are still working remotely in 2024, and you never return to NY for meetings, training, etc., then your 2024 wages are not subject to NY tax. But if you return to the company HQ for even one day of training or meetings, then all your wages for the year are taxable in NY.
You haven't told us what you do or if you are still working for that company, although it seems that you might be from the wording of your question. If you are subject to the convenience of the employer rule, then all your income might be taxable in NY, not just the part reported on the W-2. If you are not subject to the rule, you can manually adjust the amount that you report as part-year income, if it is different than the W-2.
@TomD8 is also an expert on the convenience of the employer rule.
