Because you moved from Oregon to New York, you will have to file a Part-Year return for each state. Your unemployment through September will be reported normally, but the amount received after you moved will be Oregon source income received as a nonresident. The same amount will be included as New York resident income, but you will apply the credit for tax paid to another state on the New York return.
Please ask of you have other questions, this situation is common because of the pandemic and the state rules can be confusing.
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