[Feature Request] Add support for GitHub Models

[ShiinaKin]

🥰 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