Prepare your nonresident New York return. Then prepare your Utah resident return. Utah allows a credit for income taxed by NY.
If you prepare the NY return first, TurboTax will automatically carry the NY income and tax over to UT.
New York follows the "convenience of the employer rule", meaning you may still be liable for NY tax as a remote employee if your physical office location is NY, which was your situation.
You may not get a NY refund (it depends on much much tax was withheld). However NY has one of the highest US state tax rates so you will probably not owe any UT tax.
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