refactor: use uv for dependency management

Dockerfile

@@ -2,14 +2,19 @@ FROM python:3.11-slim
 
 WORKDIR /app
 
+# Install uv
+RUN pip install uv
+
 # Install system deps
 RUN apt-get update && apt-get install -y \
     ffmpeg \
     && rm -rf /var/lib/apt/lists/*
 
-# Install Python deps
-COPY backend/requirements.txt .
-RUN pip install --no-cache-dir -r requirements.txt
+# Copy project files
+COPY backend/pyproject.toml backend/requirements.txt ./
+
+# Install dependencies using uv
+RUN uv pip install --system -r requirements.txt
 
 # Copy code
 COPY backend/ ./backend/