You did not tell us which state you are a resident of. Some states refunded the amount automatically. Some require an amendment. Some people will not receive a refund because they did not actually pay any tax on the first $10,200 of unemployment.
You can look up your state income tax department on the internet and contact them in regard to your question about whether and when you are going to receive a refund of state paid on the unemployment exemption.
DO I NEED TO AMEND MY STATE RETURN FOR UNEMPLOYMENT?
You *might* need to amend your state return for unemployment that was taxed by your state.