Update LiteLLM provider for v4

[areibman]

IMPORTANT: Open a PR basing your branch off redesign to merge onto redesign

Requirement: Also raise a PR to Litellm's docs https://docs.litellm.ai/docs/observability/helicone_integration

[areibman]

Suggested: Use the callbacks provided in similar examples like Langfuse

[Dwij1704]

Will need to add an instrumentor for LiteLLM as openllmetery doesn't have one.
We can take reference from Openlit

[Dwij1704]

Raised a PR for litellm docs BerriAI/litellm#9561
Preview link

[Dwij1704]

LiteLLM Integration Feedback Report

Current Situation

• LiteLLM has rejected our PR due to dependency concerns for proxy users
• They prefer an approach similar to Langsmith's integration model
• The core issue is requiring additional dependencies that proxy users cannot use

How Langsmith Handles Integration

From Langsmith's documentation:

1. They support multiple integration paths:
   • Direct HTTP-based logging via their core integration 🔗
   • OpenTelemetry integration as an optional feature 🔗
   • Client-side trace exporter for advanced use cases 🔗

[Dwij1704]

Raised another PR with the changes requested, here is a preview of the document