feat: add BurnCloud as new AI model provider

[rustburn]

Description

This PR adds support for BurnCloud API as an alternative model provider, offering stable and cost-effective access to leading AI models.

More Information

• BurnCloud API integration with OpenAI-compatible endpoints
• Support for multiple model families:
• Claude 4.0/3.7/3.5
• GPT 4o/4o-mini/o1/4.5 preview/o1-mini
• GPT-image-1
• Gemini 2.5 pro/2.0
• DeepSeek R1/V3
• Base URL: https://ai.burncloud.com/v1
• Compatibility: Full OpenAI API format compatibility
• Authentication: Standard API key authentication
• API Service: https://ai.burncloud.com
• Website: https://www.burncloud.com

Validation

• API connection tested
• Model responses validated
• Error handling implemented
• Documentation updated

Linked Issues

N/A

[CLAassistant]

All committers have signed the CLA.