refactor: use uv sync with lock file

Dockerfile

@@ -3,23 +3,27 @@ FROM python:3.11-slim
 WORKDIR /app
 
 # Install uv
-RUN pip install uv
+COPY --from=ghcr.io/astral-sh/uv:latest /uv /uvx /bin/
 
 # Install system deps
 RUN apt-get update && apt-get install -y \
     ffmpeg \
+    git \
     && rm -rf /var/lib/apt/lists/*
 
 # Copy project files
-COPY backend/pyproject.toml backend/requirements.txt ./
+COPY backend/pyproject.toml backend/uv.lock ./
 
-# Install dependencies using uv
-RUN uv pip install --system -r requirements.txt
+# Install dependencies using uv sync
+RUN uv sync --frozen --no-install-project
 
 # Copy code
 COPY backend/ ./backend/
 COPY frontend/ ./frontend/
 
+# Install project
+RUN uv sync --frozen
+
 EXPOSE 8000
 
-CMD ["python", "backend/main.py"]
+CMD ["uv", "run", "python", "backend/main.py"]