Integrate Unify into LiteLLM

Description

This issue tracks the process of facilitating this integration and ensures our repository is ready for incorporation into LiteLLM.

Objectives

• [ ] Evaluate the compatibility of Unify with LiteLLM
• [ ] Identify any potential conflicts or dependencies
• [ ] Determine the best method for integration (e.g., submodule, direct code import, package dependency)
• [ ] Create a plan for the integration process
• [ ] Implement the integration
• [ ] Update documentation to reflect the new integrated features
• [ ] Ensure all tests pass after integration
• [ ] Review and update CI/CD pipeline if necessary
• [ ] Create examples/demos highlighting new capabilities of LiteLLM.

Resources

• LiteLLM GitHub: https://github.com/BerriAI/litellm
• Relevant documentation: https://docs.litellm.ai/docs/
• Team members to consult: @iamjameskeane @paras55