What your work told you is correct, your work location is NY, so technically you need to pay NY taxes.
Here's a link to New York's memorandum on its "convenience of the employer" tax doctrine regarding non-resident telecommuters: https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
Pennsylvania, Nebraska, Delaware and New Jersey have the same rule. For guidance see: http://www.journalofaccountancy.com/issues/2009/jun/20091371.html
Q. Is there any way that I enjoy the benefits of no income taxes in FL?
A. There is Pending NY covid legislation that may provide a little relief. See https://taxnews.ey.com/news/2020-1411-new-york-senate-[product%20key%20removed]-businesses-to-treat-...
