New York (NY) does not have a reciprocal agreement with any state. Therefore your wages would have to be reported on the New Jersey (NJ) and then a credit for taxes paid to another state would be used on the NY return. Your resident state will not tax you twice on the same income. The credit is limited to what the actual tax liability is in the foreign state or the tax your resident state would actually charge whichever is less.
The crypto gains should be on the NY return only as your resident state. You should not pay tax in NJ for the crypto transactions. When in your NJ return you should be able to make the adjustment for income that should not be taxed as a nonresident.
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