🔧 Fix frontend warnings and add diagnostic tools

Fix:
- Add type: module to package.json to eliminate ES module warning
- Create separate backend/frontend startup scripts
- Add system status check tool

New files:
- check_status.bat: Diagnose system status
- start_backend_only.bat: Start backend separately
- start_frontend_only.bat: Start frontend separately

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

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

start_backend_only.bat

@@ -0,0 +1,44 @@
+@echo off
+title QQuiz Backend Server
+color 0B
+
+echo.
+echo ========================================
+echo   Starting QQuiz Backend Server
+echo ========================================
+echo.
+
+cd /d "%~dp0backend"
+
+if not exist "venv\Scripts\activate.bat" (
+    echo Creating virtual environment...
+    python -m venv venv
+)
+
+echo Activating virtual environment...
+call venv\Scripts\activate.bat
+
+echo.
+echo Installing/updating dependencies...
+pip install -q -r requirements.txt -i https://pypi.tuna.tsinghua.edu.cn/simple
+
+echo.
+echo Running database migrations...
+alembic upgrade head
+
+echo.
+echo ========================================
+echo   Backend Server Starting...
+echo ========================================
+echo.
+echo API URL:  http://localhost:8000
+echo API Docs: http://localhost:8000/docs
+echo Health:   http://localhost:8000/health
+echo.
+echo Press Ctrl+C to stop
+echo ========================================
+echo.
+
+uvicorn main:app --host 0.0.0.0 --port 8000 --reload
+
+pause