Azure Model Router: Model ID not surfaced when using azure.chat

### Description

> This is mainly documenting issue with `azure.chat` which doesnt seem to surface modelId - I've encountered this as model router doesnt support responses API yet. Model router allows to use multiple models so would be nice to surface model id - **imo low priority as if azure migrates to responses api this should be addressed.**
> https://learn.microsoft.com/en-us/azure/ai-foundry/openai/how-to/model-router

When using Azure's Model Router with `streamText` and `includeRawChunks: true`, the actual model ID from the provider (e.g., `gpt-5-mini-2025-08-07`) is present in the raw chunks but is **not** being surfaced in:
1. The final response object's `modelId` field
2. A `response-metadata` chunk in the stream

This makes it hard to capture which model is being used.

### Reproduction Steps

1. Set up Azure OpenAI with a Model Router deployment
2. Run the following code:

```typescript
import { azure } from '@ai-sdk/azure';
import { streamText } from 'ai';
import 'dotenv/config';

async function main() {
  const result = streamText({
    model: azure.chat('model-router'),
    prompt: 'Say where is copenhagen in three words max',
    includeRawChunks: true,
  });

  for await (const chunk of result.fullStream) {
    console.log(`[CHUNK ${chunk.type}]`, chunk);
  }

  const response = await result.response;
  console.log('--- final response ---');
  console.log('modelId:', response.modelId);
  console.log('response headers:', response.headers);
}

main().catch(console.error);

``` 

The final `response.modelId` is an **empty string** `''` However, the raw chunks **DO contain** the correct model ID in the `model` field

### Output Evidence

**Raw chunks show the correct model:**
```javascript
[RAW CHUNK] {
  choices: [
    {
      content_filter_results: [Object],
      delta: [Object],
      finish_reason: null,
      index: 0,
      logprobs: null
    }
  ],
  created: 1762017449,
  id: 'chatcmpl-CX9WD0BvOJnVehlaLGhL3kmiMTieD',
  model: 'gpt-5-mini-2025-08-07',  // ✅ Model ID is here
  obfuscation: 'siXfYsnhLGa8oW',
  object: 'chat.completion.chunk',
  system_fingerprint: null,
  usage: null
}
```

**The finish-step chunk shows empty modelId:**
```javascript
[CHUNK finish-step] {
  type: 'finish-step',
  finishReason: 'stop',
  usage: { /* ... */ },
  providerMetadata: { /* ... */ },
  response: {
    id: '',
    timestamp: 1970-01-01T00:00:00.000Z,
    modelId: '',  //  Empty instead of 'gpt-5-mini-2025-08-07'
    headers: {
      'x-ms-deployment-name': 'model-router',
      'x-ms-modelrouter-llm-deployment': 'NA',
      'x-ms-modelrouter-request-id': 'f7760d6b-423d-460a-9099-3e44b6a78a6b',
      // ...
    }
  }
}
```

**And the final response also shows empty:**
```typescript
--- final response ---
modelId:   //  Empty string
response headers: {
  'x-ms-deployment-name': 'model-router',
  'x-ms-modelrouter-llm-deployment': 'NA',
  // ...
}
```


### AI SDK Version

- `ai`: 6.0.0-beta.92
- `@ai-sdk/azure`: 3.0.0-beta.48
- Test date: November 1, 2025
- Azure Model Router deployment with `gpt-5-mini-2025-08-07` as the selected model


### Code of Conduct

- [x] I agree to follow this project's Code of Conduct

Labels: bug, ai/provider, provider/azure
State: closed