I wonder if that’s the result of influence from Idaho. ITD formally refers to their state-designated routes as State Highways, though apparently other monikers are common enough:
SH
SH stands for state highway or an Idaho route. SH 55 is also referred to as Idaho 55 or ID-55. The Idaho Transportation Department (ITD) takes care of interstates, U.S. routes and state highways (SH) in Idaho.
For its part, WSDOT headquarters seems to distinguish between state highways as infrastructure that carries state routes as designations. (I’ve lived in two states where the DOT the same distinction.) And SR is the standard abbreviation in that case. But regardless, I think the real question is whether “WA 21” or “Washington 21” is the most suitable form for data consumers to present to users in text or voice guidance, whether by regurgitating what’s in the way ref or by pretty-printing the route relation’s tags, since parsing way refs has been frowned upon for ages.