I live and work in Washington and do not owe Oregon a dime.

I desperately need the money for my down payment.

And when you write "I", you mean "my client"?  Some of us were born at night, but not last night.

Can't wait an entire year to file tax return seeking refund. 

She only got 1 paycheck---she's paid monthly

This happened earlier this month?  She made enough in January 2022 to have $4,000 state tax withheld?  When she is paid only once a month?  This is all very strange.