@Nev4tax. That is why you want to do the part-year return. New York will not "automatically" question your domicile; people move all the time. But if you filed a full-year return, they will insist that all of your income is taxable in New York when it isn't. If you have already filed a full-year resident return (IT-201), you will want to file an amended return so that it is a part-year return instead.
But filing a return is a requirement. Just having withholdings deducted from your pay does not mean that you don't file a return because you've "paid enough". Filing a tax return is a required reconciliation. And if you are entitled to a refund, New York will send that refund to you. (If you don't provide bank information for direct deposit, they would automatically send a check to the address you provide on your return).
And, you are correct to stop New York withholding. If you were working from home, you might (and probably would) still have a New York tax liability (as a nonresident, if you no longer have a NY domicile or abode). But with a Florida bona-fide office location, your income becomes Florida-sourced (no state tax) and not New York sourced.
To answer your last question, if you moved in 2021, you will file a part-year New York return in 2021, not a full-year return. Florida has no state individual income tax, so you will not need to file an individual return for Florida.
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