Yes, you need to wait until the federal return is processed to amend, but you noted the return was accepted, so you can proceed to do that as soon as the 2024 federal amended tax return form 1040-X is available for filing in TurboTax. Use this tool to check availability of forms, including 1040X: Tax form availability
Since NY didn't accept your first return that was not correct, you should proceed to correct your federal return, then address the missing IT-360. Attempting to fix the NY return prior to amending the federal 1040 is not advisable, since the starting point for state return's is federal.
Your steps are 1. Correct Federal Return 2. Correct NY.
