feat: update README and config to support custom providers with API k… (#577)

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.

README.md

@@ -97,12 +97,19 @@ export OPENAI_API_KEY="your-api-key-here"
 > - deepseek
 > - xai
 > - groq
+> - any other provider that is compatible with the OpenAI API
 >
 > If you use a provider other than OpenAI, you will need to set the API key for the provider in the config file or in the environment variable as:
 >
 > ```shell
 > export <provider>_API_KEY="your-api-key-here"
 > ```
+>
+> If you use a provider not listed above, you must also set the base URL for the provider:
+>
+> ```shell
+> export <provider>_BASE_URL="https://your-provider-api-base-url"
+> ```
 
 </details>
 <br />

codex-cli/src/utils/config.ts

@@ -76,6 +76,12 @@ export function getApiKey(provider: string = "openai"): string | undefined {
     return process.env[providerInfo.envKey];
   }
 
+  // Checking `PROVIDER_API_KEY feels more intuitive with a custom provider.
+  const customApiKey = process.env[`${provider.toUpperCase()}_API_KEY`];
+  if (customApiKey) {
+    return customApiKey;
+  }
+
   // If the provider not found in the providers list and `OPENAI_API_KEY` is set, use it
   if (OPENAI_API_KEY !== "") {
     return OPENAI_API_KEY;