fix(openai): expose azure_deployment on LLM and fix model property fallback

[tsushanth]

Closes #6209

When calling LLM.with_azure() without an explicit model argument, the model property on the returned instance returned "unknown" even when azure_deployment was set. This happened because the model fallback in with_azure() previously hard-coded a default and the model property had no awareness of azure_deployment.

This change adds azure_deployment to _LLMOptions so it is tracked independently of model. The with_azure() factory now stores the azure_deployment value in opts rather than using it to silently fill in model. The model property is updated to fall back to azure_deployment when model is None, and a new azure_deployment property is exposed so callers can inspect the value directly.

The LLM.__init__ signature is updated to accept None for model to support the Azure path cleanly without overloading the default.

[devin-ai-integration]

Devin Review found 3 potential issues.

[devin-ai-integration]

🔴 Passing None model to LLMStream causes TypeError crash in Azure path

When LLM.with_azure() is called without specifying model (which now defaults to None), the chat() method at line 1031 passes self._opts.model (which is None) directly to LLMStream. This propagates through the openai plugin's LLMStream.__init__ into the inference LLMStream.__init__ (livekit-agents/livekit/agents/inference/llm.py:378), which calls drop_unsupported_params(model, ...). Inside that function (livekit-agents/livekit/agents/inference/llm.py:85), the expression "/" in model raises TypeError: argument of type 'NoneType' is not iterable because model is None.

The model property (line 186) already handles the None case correctly by falling back to azure_deployment or "unknown", but the chat() method bypasses the property and reads self._opts.model directly.

(Refers to line 1031)

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[devin-ai-integration]

🚩 Breaking change: with_azure model default changed from "gpt-4o" to None

The model parameter default in with_azure changed from "gpt-4o" to None (line 199). This is a behavioral change for existing callers who relied on the implicit default model. Previously, LLM.with_azure(azure_deployment="my-deployment") would still send model="gpt-4o" to the API. Now it sends None (or after the bug fix, sends the azure_deployment value). This is likely the intended behavior since Azure users typically specify deployment names rather than model names, but it's a breaking change for users who relied on the old default.

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[devin-ai-integration]

🚩 Setting azure_deployment after construction bypasses validation

At line 261, azure_deployment is set directly on _opts after the LLM instance is already constructed (llm._opts.azure_deployment = azure_deployment). This means the __init__ method doesn't know about the deployment during construction (it sees azure_deployment=None). This pattern works but is fragile — any future logic in __init__ that needs to consider azure_deployment would be bypassed. Additionally, azure_deployment could itself be None if the caller doesn't pass it, making both model and azure_deployment None, resulting in the model property returning "unknown".

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