What you've described indicates you remain domiciled in New York even though you spent part of the year in another state. You are more closely associated with New York due to school, you returned to New York and will work remotely in New York before moving to another state in 2021. Your residency status for 2020 for New York is a full year resident of New York and a non-resident of the state you lived and worked in from March to August.
Your residency at the end of 2021 will depend again on whether your intention is to return to New York or not. If your intention is to return to New York after working onsite, your residency would remain a New York resident and be a non-resident of the state you are working in onsite.
What is my New York Residency
