I am currently in a similar situation as I moved from NY to CT in August 2022 while working from home the entire year. Employer is located in NYC meaning I paid NY and NYC taxes but I didn't pay CT taxes. Turns out that about half of the withhold NYC taxes for the year will be refunded due to change in status from residential to non-residential. I didn't have to pay CT taxes because I already paid NY taxes. Unlike NY, CT doesn't have local income taxes so this was a win-win situation for me.
