As apsec112 mentioned it's up to the state. And in this case Washington state has a very clear constitution and case law history that prohibits non uniform taxes, like a progressive income tax:
> All taxes shall be uniform upon the same class of property within the territorial limits of the authority levying the tax and shall be levied and collected for public purposes only
That means any state law, municipal ordinance, etc, that violates that provision is going to be struck down on review. So there could be a tax that applies to income differently than real property or other assets. But the tax would have to be applied in a uniform manner across all levels of income, or uniformly against property of different values, etc.
And that history and nuance matters because Seattle cant tax income at differential rates. But they can tax businesses in a uniform manner. And assuming section 5.38.030.B passes the "uniform" and "property" challenges they can achieve almost the same thing as a municipal progressive income tax.
Washington State Constitution Article VII Section 1 https://ballotpedia.org/Article_VII,_Washington_State_Consti...
Here's a slightly dated article that has a good overview of the history https://digitalcommons.law.seattleu.edu/cgi/viewcontent.cgi?...