You file part-year returns for both Maryland and DC. The part-year Maryland return will only claim the income you earned while living in Maryland. Since you had Maryland tax withheld the entire year, this should result in a significant refund. But this is "rob Peter to pay Paul", because you will likely owe most of this refund to DC (since you have not had DC tax withheld).
Yes, you want to make sure you have your tax withholdings adjusted accordingly. Because of the reciprocal agreement, you no longer want to have Maryland taxes withheld, and if you don't move back to Maryland will not have to file a 2022 return for Maryland.
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