State tax filing

Hello,

I am in a similar situation. I work for a NY company and just moved from NY to WA as of Sept 2021. My work in state is NY and live in state is WA; I will be working remotely from WA. I noticed my paycheck was taxed as if I live in NY. Based on what I am reading, I will need to file a federal tax return, a NY state return and WA state return. Do you know if I will receive a tax credit from WA from Sept 2021 to Dec 2021? Or will I still have to pay NY state tax even though I moved to WA now where there is no state income tax?