Just try using ux with Google Artifact Registry and AWS CodeArtifact. You need the username in the URL with GAR and you need it in the environment variable with AWS. I'm not sure who's causing the pain with using uv with private repositories (but I'd bet it's uv), but they are selling a solution to that pain.
Full disclosure, uv rocks and is way better than poetry, setuptools and whatever complicated and non-zen way packaging python has had in the past.
In my experience (albeit from about 4 years ago) having some kind of private package with pipenv (or even plain pip) was really annoying. We went the route of a private repo on Github rather than a private package repository, which maybe set us up for exactly that annoyance.
Full disclosure, uv rocks and is way better than poetry, setuptools and whatever complicated and non-zen way packaging python has had in the past.