Does a state tax refund paid in 2023 for work done in 2022 count as out of state work in 2023?

If you received a refund from your state for taxes you had withheld from your wages, this would not count as work.  This is the same thing as getting a refund from the federal government.  

So, if I am understanding correctly, that you had a job and had state taxes withheld, then got a refund of those taxes, this would be a refund and would not be entered as any type of work done.

This refund would ONLY be taxable if you took the itemized deduction in 2022 and took a deduction for your state and local taxes.  Otherwise, this does not get entered anywhere on your return.