Add Default Headers to LiteLLM Provider

[andrewshu2000]

Overview

Add support for sending default headers with all LiteLLM API requests to track the originating app, ensuring consistent header usage across all API providers.

Problem Statement

Currently, when using LiteLLM as an API provider, the default headers that track the originating app (HTTP-Referer and X-Title) are not being sent with requests. These headers were added in PR #1300 for other providers but were missed for LiteLLM. This inconsistency means we cannot properly track which requests are coming from our application when using the LiteLLM provider.

Proposed Solution

Modify the LiteLLM provider implementation to include the default headers in all API requests:

1. Update the RouterProvider class to include DEFAULT_HEADERS in the OpenAI client initialization
2. Update the LiteLLM model fetcher to include DEFAULT_HEADERS in axios requests
3. Update tests to verify this behavior

Benefits

• Consistent header usage across all API providers
• Improved request tracking and analytics
• Better debugging capabilities when investigating API issues
• Proper attribution of API usage to our application