For the Other Wage Adjustments - W-2 you should be able to determine if you had any forms of compensation that require a NJ adjustment from your W-2.
Dependent care benefits are reported in Box 10 and would have to be added to NJ income. Adoption benefits are reported in Box 12 with Code T. Box 12 Codes E, F, G, or H denote various non-401(k) retirement plan contributions that would have to be added to your NJ income. If you see an amount in Box 14 or on the top of your W-2 that says CAFE 125 or something like that, that would be contributions to a cafeteria plan that would need to be added. You can probably find the same information on your paystubs as well. I think by doing the NJ + NY - Federal you would only end up with the excess from October on.
Removing the NJ wages was correct. It makes sense if you were telecommuting, or if your company taxed you like you were a telecommuter. With the ending of the pandemic, New Jersey stated that people working from NJ would be taxed by their home state beginning October 1, no matter where their employer location was.
New York requires its employers to withhold tax for NY no matter where their employees are located with few exceptions.
