**SOLUTION**
@sterndata : “directory privacy” for the public_html folder was turned ON- once it was turned off, everything worked as it should.
This is not something I ever payed attention to- should some directories be set to private, or is that only if there are other site users with some kind of access to the root directory of the site?
So, my hosting provider (GreenGeeks) set up a test wordpress installation, and said all was working as it should with the login. I still got a server-based login dialog when I tried from my location, so we’ll see what they make of that.
This is as installed- I have not edited .htaccess.
I thought it was strange that I did not see the typical WP login page, but I can’t figure out why it would be this way out of the gate, unless my hosting provider has some insight (waiting for a response).