### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

Not all the models/reasoning are listed for github_copilot provider. Here is the list from vscode model selector:

<img width="783" height="425" alt="Image" src="https://github.com/user-attachments/assets/f6787a89-4b58-48c8-9f2a-3c7488654236" /> And, for example, gpt-5 mini, gpt-5.4, gpt-5.4-mini supports reasoning.

Here is what I get from litellm:

<img width="895" height="379" alt="Image" src="https://github.com/user-attachments/assets/7805f7b1-1d0a-439e-8e61-add8d1ef2260" />

I can configure gpt-5.4 with: ``` model_list: - model_name: gpt-5.4 litellm_params: model: github_copilot/gpt-5.4 order: 10 model_info: mode: responses ```

But still i get errors about not suppoting tool calls with reasoning, even if I set base_model to either gpt-5.4 or azure_ai/gpt-5.4

### Steps to Reproduce

1. Try to add model with github_copilot provider

### Relevant log output

```shell

```

### What part of LiteLLM is this about?

Proxy

### What LiteLLM version are you on ?

v1.87.0

### Twitter / LinkedIn details

_No response_