It's about whether you've been to Europe at all in the 14 days preceding, not about whether your immediate origin was European.

And for Schengen, you'll have a stamp in and out (assuming 1 passport).

No Schengen stamps if you already live in the Schengen area. Unless there is data sharing the US gov wouldn’t be able to see it from a passport.

I suppose it will be another question on the form. Next to ‘I am not a terrorist’

As a side-note: I saw the forms that my great grandparents had to fill out when entering the US from Europe back in 1905 or thereabouts. There was a checkbox for "anarchist"

Plus ça change, plus c'est la même chose

The ban is on the Schengen area, which does include the Azores.

I live on an island. There are all sorts of weird legal things that play out on these bits of rock. I suspect that there are all sorts of lawyers reading interesting bits of definitions of treaties and history right now.

The Azores is part of Portugal, which is on the travel ban list.

They don't need to be routed through a non-European destination. Crew are exempt. The airlines will just deny boarding to people subject to the ban (which is non-exempt people who have been in Schengen in the last 14 days, not people who just came from there).

It's not a flight ban it's based on the physical presence of the traveller

The Azores are in Europe.

or Britain, or Turkey

Turkey is also erecting public event suspension (trade fairs and large ceremonies cancelled by today), so not going to work.

doesn't mean you can't fly to the US from there.