Waiting on Washington Plates

Took delivery a couple of months ago and been running on the Illinois paper plate, which expires end of this month. I recieved the vehicle title a few weeks ago in the post, so address etc is all correct. Decided to text "Carlton" yesterday to chase my proper plates. Received a reply saying I should contact "my local DMV to get replacement plates".

Very naive, and new to US/Washingon - do I just contact DMV, or looking online suggests I need to go to a 3rd party office for plates? Can anyone help with direction on that? Eternally grateful as Google is not inspiring my confidence in which direction to go.

Second question - $90k cash payment for a car, this is terrible service right? Register my car for me, don't dump the process onto me. Should I be grumpy and push back on this? My experience with the car is near 100%, but with the registration process not good (they needed to do online JP process which was not possible as I have no credit history in the US, making the pickup quite stressful).

(Picture for engagement only)