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Not here either on my Pixel 2. I'm on the P beta...wonder if that makes a difference.
 
I have it on my Pixel Xl, running P dev preview 3. I believe its a server side thingy.
I got a prompt from Messages app after I read this thread. Not sure if I solicited it though. Seems to work ok. However I have been using MightyText for some time and it opens a window with new message sent. Messages just sends a general notification to pc.
 
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