fix: auto-add provider prefix for custom LLM endpoints

LiteLLM requires model names in format "provider/model-name".
When LLM_API_BASE is set, automatically prefix model with "openai/"
if no provider prefix is present.

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

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

backend/.env.example

@@ -44,6 +44,20 @@
 # LLM_API_BASE=http://localhost:8000/v1
 # LLM_API_KEY=your-key
 # LLM_MODEL=qwen2.5
+# Note: When LLM_API_BASE is set, model is auto-prefixed as "openai/qwen2.5"
+
+# =============================================================================
+# Model naming convention (LiteLLM requires provider prefix)
+# See: https://docs.litellm.ai/docs/providers
+# =============================================================================
+# Format: provider/model-name
+# Examples:
+#   openai/gpt-4
+#   anthropic/claude-3-haiku-20240307
+#   gemini/gemini-pro
+#   ollama/llama2
+#   huggingface/starcoder
+#   azure/your-deployment-name
 
 # =============================================================================
 # Force mock mode (no API calls, uses predefined responses)

backend/app/llm.py

@@ -76,6 +76,13 @@ class LLMService:
         self._mock_mode = os.environ.get("LLM_MOCK_MODE", "").lower() == "true"
         self._acompletion = None
 
+        # Auto-add provider prefix for custom endpoints
+        # LiteLLM requires format: provider/model (e.g., openai/gpt-4)
+        # See: https://docs.litellm.ai/docs/providers
+        if self._api_base and "/" not in self._model:
+            self._model = f"openai/{self._model}"
+            logger.info(f"Auto-prefixed model name: {self._model} (custom endpoint detected)")
+
         if self._mock_mode:
             logger.info("LLMService running in MOCK mode (forced by LLM_MOCK_MODE)")
             return