@unknownzack I agree with @kristinelbly that you were not a NYC or NYS resident for 2021, and should file IT-203 as a New York nonresident. Since New York City does not tax nonresidents, at the very least any New York City withholdings should be refunded. And it does not surprise me that your company's payroll processing is challenged on how to change your withholdings, because of New York's requirements for employer withholding.
Having said this, I think it is wise that if you take a position that your income to be not taxable to New York State, that you disclose why you are doing so. This entire thread contains a very enlightening discussion on the subject, and one of my biggest takeaways is what often happens with taxing issues: facts and circumstances dictate. When you work from home on behalf of a New York office, the tax department's first inclination will be to state your income is taxable in New York. So you may be asked to prove otherwise. With total respect to kristinelby's clear experience and in-depth knowledge of the subject, I'm also willing to go out on a limb to state that more often than not, New York questions this position for the reasons @TomD8 states above.
One situation in which I feel you probably have an argument is if your work in Florida, while on behalf of the New York office, is directed primarily at non-New Yorkers. But if working virtually for a New York office is business directed at New Yorkers or for a New York interest, I have to believe the state does not believe you to be working "without" New York.
Main thing is to understand: if you say you didn't work in New York, you will probably have to defend your position, and you may not win. But you shouldn't pay NYC tax regardless.
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