[Bug]: User-Agent header is not being sent in HTTP/1.1 requests to Docker registries

### I have done the following

- [x] I have searched the existing issues
- [x] If possible, I've reproduced the issue using the 'main' branch of this project

### Steps to reproduce

Proxy the requests and watch them

### Problem description

User-Agent is a *SHOULD* header according to the HTTP/1.1 RFC, and not a *MUST*, but it really should be set

### Environment

```markdown
- OS: macOS 26.5
- Xcode: 26.5
- Container: 0.12.1.0
```

### Code of Conduct

- [x] I agree to follow this project's Code of Conduct

Start by reproducing the issue with a proxy and watching HTTP/1.1 requests sent to Docker registries. Trace where those requests are constructed and verify that the completed requests include a User-Agent header.

Written by the indexing model from the issue text.