This can be a bigger deal if your insurance lapses (can be a big fine in states with a system that tracks that) or you get in an accident & your insurance won't cover you because it's the wrong state. Some states are absolutely insane about this stuff (Virginia is one I know is, no idea about Utah- WA is pretty lax about it in my experience) but keep all records of changing your insurance & title (old & new) & reg etc. etc. Some make you send in plates (not sure how enforced that is?) Some go after you 7 yrs from when you moved & will put a hold on your license so you can't renew & need a lawyer & a bunch of paperwork to get it corrected even though you lived in that state for less than a month oy vey.

Just get it registered & license renewed for WA - they have no idea when you got there & they honestly don't care as long as you are actively getting it registered & insured in the correct state.