[Bug]: LiteLLM Instrumentation not working for Responses API

### Contact Details

_No response_

### 📦 Package Version

0.4.14

### 🎞️ Framework Version

1.72.0

### 🔎 Describe the Bug

Neither normal instrumentation with LiteLLM or using the success_callback arg are working properly for LiteLLM for `litellm.response` (they work for `litellm.completions`).
Success callback not working (see docs https://docs.litellm.ai/docs/observability/agentops_integration):

```
In [1]: import agentops
i
In [2]: import litellm

In [3]: litellm.success_callback = ["agentops"]

In [4]: agentops.init(auto_start_session=False)
...:

In [5]:
...:
...: # Non-streaming response
...: response = litellm.responses(
...: model="openai/gpt-4o",
...: input="Tell me a three sentence bedtime story about a unicorn.",
...: max_output_tokens=100
...: )
...:
...: print(response)
````
-> No trace detected in AgentOps dashboard

As well as normal instrumentation:
```
In [3]: agentops.init()
🖇 AgentOps: Session Replay for default trace: https://app.agentops.ai/sessions?trace_id=24108c993e0f3b8b4d20b3e0b7e96c06
Out[3]:

In [4]: import litellm

In [5]:
...: # Non-streaming response
...: response = litellm.responses(
...: model="openai/gpt-4o",
...: input="Tell me a three sentence bedtime story about a unicorn.",
...: max_output_tokens=100
...: )
...:
...: print(response)
```

TODO:
1. Fix instrumentation
2. Update AgentOps docs if required
3. Raise a PR and update LiteLLM's AgentOps docs if required

### 🤝 Contribution

- [ ] Yes, I'd be happy to submit a pull request with these changes.
- [ ] I need some guidance on how to contribute.
- [ ] I'd prefer the AgentOps team to handle this update.