You do seem to meet the DC definition of a statutory resident. As such, all of your income for the entire year is taxable to DC as a resident. You will need to prepare the DC return first, and, if you were also a resident of California (maintained your domicile in California and returned there), you may claim a credit on your California return for tax you pay to DC.
If you did not maintain a domicile in California, you may file California as a nonresident instead. In this situation, you prepare the California return first, and you only claim income you received while physically present in California.
The unemployment income is taxed in DC, unfortunately, because a resident state (DC acts like a state for this purpose) is allowed to tax all of your income from all sources. Some states consider unemployment compensation that has been derived from a job within the state as taxable to the state, and many others do not. California obviously does not because they don't tax the income anyways. But it still is taxable in DC (above $10,200).
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