feat: add multi-provider LLM support with LiteLLM

- Replace openai with litellm for unified LLM interface
- Support 100+ providers: OpenAI, Anthropic, Gemini, Azure, Ollama, etc.
- Add custom API base URL support (LLM_API_BASE)
- Add .env file support with python-dotenv
- Add .env.example configuration template

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

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/.env.example

@@ -0,0 +1,51 @@
+# LLM Configuration for The Island Backend
+# Copy this file to .env and fill in your values
+
+# =============================================================================
+# Option 1: OpenAI (default)
+# =============================================================================
+# OPENAI_API_KEY=sk-xxx
+# LLM_MODEL=gpt-3.5-turbo
+
+# =============================================================================
+# Option 2: Anthropic Claude
+# =============================================================================
+# ANTHROPIC_API_KEY=sk-ant-xxx
+# LLM_MODEL=claude-3-haiku-20240307
+
+# =============================================================================
+# Option 3: Google Gemini
+# =============================================================================
+# GEMINI_API_KEY=xxx
+# LLM_MODEL=gemini/gemini-pro
+
+# =============================================================================
+# Option 4: Azure OpenAI
+# =============================================================================
+# AZURE_API_KEY=xxx
+# AZURE_API_BASE=https://your-resource.openai.azure.com
+# LLM_MODEL=azure/your-deployment-name
+
+# =============================================================================
+# Option 5: OpenRouter (access multiple models)
+# =============================================================================
+# OPENROUTER_API_KEY=sk-or-xxx
+# LLM_MODEL=openrouter/anthropic/claude-3-haiku
+
+# =============================================================================
+# Option 6: Local Ollama
+# =============================================================================
+# OLLAMA_API_BASE=http://localhost:11434
+# LLM_MODEL=ollama/llama2
+
+# =============================================================================
+# Option 7: Custom/Self-hosted (OpenAI-compatible endpoint)
+# =============================================================================
+# LLM_API_BASE=http://localhost:8000/v1
+# LLM_API_KEY=your-key
+# LLM_MODEL=qwen2.5
+
+# =============================================================================
+# Force mock mode (no API calls, uses predefined responses)
+# =============================================================================
+# LLM_MOCK_MODE=true