No, it will not effect your federal return and New York has started accepting e-filed returns.
You are able to e-file your state separately using the instructions given above. It is possible that one of the forms you need is not ready or not available to be e-filed.
To check NYS form availability in TurboTax, please see NYS Individual Form Availability
From your description, it does not seem like this would be the issue, however, since you had no problems in the past and had a similar tax situation in 2020. What do you have on your return besides a W-2?
@Scottryan1010
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