[Bug]: OpenAI provider prefix stripped twice for namespaced model IDs in Responses API

Bug Description

LLMProvider.from_model() parses a model string like openai/openai/example-model into model="openai/example-model" + provider="openai". When as_litellm_call_kwargs() forwards that as model="openai/example-model" + custom_llm_provider="openai", LiteLLM's Responses API path re-parses and strips the openai/ prefix again, sending example-model upstream and causing 400 Model not found.

This also affects any namespaced model ID whose inner segment is a LiteLLM provider name (e.g. openai/openai/o3-mini, mistral/mistral/large).

Upstream report: OpenHands/OpenHands#16365

Expected Behavior

The SDK should pass a model string that, after LiteLLM re-parses it, resolves to the originally parsed openai/example-model.

Actual Behavior

Before the fix, running the repro path through as_litellm_call_kwargs() sends example-model to the upstream endpoint. The upstream returns 400 Model not found because the model identifier has lost its provider namespace.

uv run pytest tests/sdk/llm/test_litellm_provider.py::test_llm_provider_preserves_namespaced_model_after_litellm_reparse -v

The regression test above (introduced in the fix) fails on main and passes after the change.

Acceptance Criteria

• LLMProvider.as_litellm_call_kwargs() re-adds the provider prefix when self.model already starts with it, so LiteLLM strips exactly one prefix and lands on the correct parsed model.
• uv run pytest tests/sdk/llm/test_litellm_provider.py -v passes.
• Existing nested-provider cases (openrouter, bedrock, mistral, litellm_proxy) continue to pass.

Start with LLMProvider.as_litellm_call_kwargs() and run tests/sdk/llm/test_litellm_provider.py::test_llm_provider_preserves_namespaced_model_after_litellm_reparse. Review the existing nested-provider tests, then verify the full test file and confirm that namespaced models retain the correct identifier after LiteLLM reparses them.