[Feature Request] Add support for `GitHub Models`

### 🥰 Feature Description

I hope to add support for `GitHub Models` to the provider. While they use the OpenAI protocol, utilizing the `custom interface` would override the standard OpenAI properties.

### 🧐 Proposed Solution

It seems like a good strategy to reuse the existing OpenAI codebase for GitHub Models by modifying variable names.

Referring to issue #5336 for context is helpful.
Alternatively, waiting for the completion of #4030 might offer a more comprehensive solution.

### 📝 Additional Information

_No response_