No. Washington state is no longer your resident state if you left the U.S. in October 2022.
TurboTax wants to know your residence as of year-end. Choose Foreign or U.S. Possession at the bottom of the dropdown list in State of residence (on December 31, 2022).
As for documentation, you will have to file a U.S. tax return if you had U.S. income in 2022.
You are dual-status because you were a U.S. resident who became a non-resident.
TurboTax does not handle dual-status returns. Contact TurboTax partner Sprintax.com to prepare your return.
See How should I file my taxes as a dual-status alien?