Add root endpoint to provide API info and health status

app/main.py

@@ -33,6 +33,18 @@ def _load_origins() -> list[str]:
 app = FastAPI(title="CrownCode Backend API", version="0.1.0")
 
 
+@app.get("/")
+async def root():
+    """Root endpoint for health check and API info."""
+    return {
+        "name": "CrownCode Backend API",
+        "version": "0.1.0",
+        "status": "running",
+        "docs": "/docs",
+        "health": "/api/health"
+    }
+
+
 @app.exception_handler(ValueError)
 async def value_error_handler(request: Request, exc: ValueError) -> JSONResponse:
     logger.warning(f"Validation error: {exc}")