?
I followed your suggestion of providing a Nuget API key, I got a different error.
I found that if I unregistered the repository in PowerShell, and reregistered it, things work as expected when you provide an API key.
It appears that Publish-Module does not work without an API key. Since ProGet will ignore it, (assuming the feed is not configured with one), you get the effect of just credential auth. (So might as well put an API key on the feed to avoid confusion.)