Surely your local blujays must have heard the hawk somewhere in order to learn its call? It figures that a hawk would occasionally show up in your neighborhood.
Machine identification can still need some manual confirmation, even though this app does a really good job. It’s not a confirmed sighting until you have a visual confirmation.
There definitely are hawks all around my area.
In this case, while I couldn't see it directly while he was making the call, I had watched him fly to and land in a nearby tree before the call and then shortly after watched it take off. So I can't be 100% sure, but I'd be willing to bet that it was the Jay.