feat(docker): restructure Dockerfile for multi-stage build

Update the Dockerfile to implement a multi-stage build process. 
Introduce a dedicated FFmpeg stage and separate development, build, 
and production stages to optimize image size and improve build 
efficiency. Add necessary dependencies and configure the 
environment for better performance. Update the .dockerignore 
to exclude sensitive files and unnecessary directories.

.dockerignore

@@ -1 +1,9 @@
-*
+**/coverage
+**/.env
+**/.aws
+**/.ssh
+Dockerfile
+docker-compose.yml
+**/.DS_Store
+**/venv
+**/env

Dockerfile

@@ -1,23 +1,58 @@
-FROM python:3.13-slim-bullseye
+# FFmpeg stage
+FROM jrottenberg/ffmpeg:4.1-scratch AS ffmpeg
 
-USER root
+# Development stage
+FROM python:3.13-bullseye AS development
 
-ARG INSTALL_GIT=false
-RUN if [ "$INSTALL_GIT" = "true" ]; then \
-    apt-get update && apt-get install -y git && rm -rf /var/lib/apt/lists/*; \
-    fi
+COPY --from=ffmpeg / /
 
-# Runtime dependency
-RUN apt-get update && apt-get install -y --no-install-recommends \
-    ffmpeg \
-    && rm -rf /var/lib/apt/lists/*
+ENV PYTHONUNBUFFERED=1 \
+  PYTHONDONTWRITEBYTECODE=1
 
-RUN pip install markitdown
+# Install build dependencies
+RUN apt-get update && apt install -y --no-install-recommends \
+  build-essential \
+  && apt-get clean \
+  && rm -rf /var/lib/apt/lists/*
 
-# Default USERID and GROUPID
-ARG USERID=10000
-ARG GROUPID=10000
+RUN pip install --no-cache-dir hatch
+
+WORKDIR /app
+COPY . /app/
+
+# Build stage
+FROM python:3.13-bullseye AS build
+
+# Install build dependencies
+RUN apt-get update && apt install -y --no-install-recommends \
+  build-essential \
+  && apt-get clean \
+  && rm -rf /var/lib/apt/lists/*
+
+RUN pip install --no-cache-dir hatch
+
+WORKDIR /app
+
+COPY pyproject.toml /app/
+COPY . /app/
 
-USER $USERID:$GROUPID
+RUN hatch build
+
+# Production stage
+FROM python:3.13-slim-bullseye AS production
+
+# Copy ffmpeg binaries
+COPY --from=ffmpeg / /
+
+WORKDIR /app
+
+COPY --from=build /app/dist /tmp/dist
+
+RUN pip install --no-cache-dir /tmp/dist/markitdown-*.whl
+
+# Default USERID and GROUPID
+RUN adduser -u 5678 --disabled-password --gecos "" appuser && chown -R appuser /app
+USER appuser
 
-ENTRYPOINT [ "markitdown" ]
+# Entrypoint
+ENTRYPOINT ["markitdown"]