Add AI Badgr as a cheaper OpenAI-compatible backend

[michaelbrinkworth]

Add AI Badgr as a cheaper OpenAI-compatible backend

This PR adds a short documentation section showing how to use AI Badgr as a drop-in replacement for OpenAI's API at a fraction of the cost.

What's Changed

• Added a new section to the README explaining how to override the base_url parameter
• Included code examples for:
  • Python (using the openai package)
  • JavaScript/Node.js (using the openai package)
  • cURL (command-line usage)
• Notes on advanced features (streaming, JSON mode)

Key Points

• Cheaper alternative - AI Badgr offers OpenAI-compatible API at significantly lower costs
• Docs-only change - No code modifications or breaking changes
• Optional provider - Developers can choose to use it or not
• OpenAI-compatible - Works with existing OpenAI client libraries (just swap the base_url)
• Simple integration - Just override base_url and optionally api_key

Technical Details

AI Badgr implements the OpenAI API specification, supporting:

• Chat completions with streaming
• JSON mode responses
• Compatible with standard OpenAI SDKs
• Same API interface, lower costs

This is an optional addition that gives developers a cost-effective alternative backend choice for their OpenAI-compatible applications.

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