You can add the noname=yes tag to avoid the validation error.

This name should be on the official_name=* tag since it is not used by the general public. This is no different than the "So and So Memorial Highway" names.

Please see this wiki article: osm.wiki/United_States/2021_Highway_Classification_Guidance#Trunk

It says that trunk should only be used on expressways (divided highways with at-grade intersections) in "areas with high population density" (i.e. urban areas). The only part of SR 99 that meets that definition is the stretch of Aurora Avenue between the north end of the SR 99 tunnel and where it hits the first stop light at the intersection with Winona Ave N on the north end of Green Lake. This section needs to also have the expressway=yes tag.