Since you moved to DC on January 1, 2022, you do not file a DC return for 2021 because you did not live in DC in 2021. Your current address needs to be the address in DC. You file the state return for the state in which you resided and earned income during 2021. If you lived in NY the entire year, then that is where you report your state income for 2021.
If you are filing a state return for NY, the county and school district would be for the county and school district that you lived in during 2021.
