[Integration] LiteLLM Provider & Gateway Support

[ishangupta-ds]

Overview

Integrate Turing Engine as a native model provider in BerriAI/litellm under the turing/* model prefix.

Key Deliverables

• Submit PR to BerriAI/litellm implementing TuringEngineConfig (integrations/litellm/turing_engine.py).
• Add routing documentation for litellm_config.yaml in docs/integrations/litellm.md.
• Verify multi-client load balancing and cost estimation.

Upstream Reference

See integrations/litellm/UPSTREAM_PR.md for the ready-to-submit PR body.

[ishangupta-ds]

🚀 Upstream Pull Request submitted to BerriAI/litellm: BerriAI/litellm#38181