feat: add BurnCloud provider with 24 AI models

Add new BurnCloud provider configuration supporting multiple AI model families:
- 5 Claude models (Sonnet 4, Opus 4, 3.5 Sonnet)
- 10 GPT models (GPT-4.1, GPT-5, GPT-4o variants)
- 6 Gemini models (2.5 Pro/Flash variants)
- 3 other models (o3, DeepSeek-V3)

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

providers/burncloud.json

@@ -0,0 +1,31 @@
+{
+  "name": "burncloud",
+  "api_base_url": "https://ai.burncloud.com/v1/chat/completions",
+  "api_key": "",
+  "models": [
+    "claude-sonnet-4-20250514",
+    "claude-3-7-sonnet-20250219",
+    "claude-opus-4-1-20250805",
+    "claude-3-5-sonnet-20241022",
+    "claude-opus-4-20250514",
+    "gpt-4.1",
+    "gpt-image-1",
+    "gpt-4o",
+    "gpt-5",
+    "gpt-4o-mini",
+    "gpt-4.1-mini",
+    "chatgpt-4o-latest",
+    "gpt-4o-2024-11-20",
+    "gpt-5-chat-latest",
+    "text-embedding-3-large",
+    "gemini-2.5-pro",
+    "gemini-2.5-flash",
+    "gemini-2.5-flash-nothink",
+    "gemini-2.5-pro-search",
+    "gemini-2.5-pro-preview-05-06",
+    "gemini-2.5-pro-preview-06-05",
+    "o3",
+    "o3-mini",
+    "DeepSeek-V3"
+  ]
+}