When using a non-built-in provider with the `--provider` option, users
are prompted:
```
Set the environment variable <provider>_API_KEY and re-run this command.
You can create a <provider>_API_KEY in the <provider> dashboard.
```
However, many users are confused because, even after correctly setting
`<provider>_API_KEY`, authentication may still fail unless
`OPENAI_API_KEY` is _also_ present in the environment. This is not
intuitive and leads to ambiguity about which API key is actually
required and used as a fallback, especially when using custom or
third-party (non-listed) providers.
Furthermore, the original README/documentation did not mention the
requirement to set `<provider>_BASE_URL` for non-built-in providers,
which is necessary for proper client behavior. This omission made the
configuration process more difficult for users trying to integrate with
custom endpoints.
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