You pay state taxes based on where you actually lived, not on where you say you lived, not on where you identify as having lived, not on what you perceive to be your main residence, and not on where you own a PO box. You pay state taxes based on where you actually lived, as in where your physical body was in space and time. And your employer obviously has this information for tax withholding.

I’m pretty sure you pay taxes to the state you physically are in while doing the work.

So if you leave NY temporarily and work remotely from FL you will no longer have income tax while you are in FL.

But then you have to prove to NY that you were in FL. States like NY and CA will claw every dollar they can from you and if they see you're getting paid to an in-state address, good luck proving you weren't actually in-state. You likely won't be able to get back the money your company automatically deducted from your paycheck.

Not tax advice, so consult your own professional preparer:

NY state has first dollar claim if your employer says your job is in NY regardless of your physical address. If, for example, you live in NJ but commute into NY, you’re paying NY state tax with no opt-out. NJ credits residents for NY taxes but then gets their money via property taxes.

NYC is even crazier, with part time residents going so far as to take daily pictures of themselves with local papers to prove that they reside outside the city more than half the year to avoid NYC income tax.

They end up having to pay NY state taxes since that's what your employer is reporting.