Speed up image build by reusing static ffmpeg

Dockerfile

@@ -5,21 +5,21 @@ RUN go mod download
 COPY backend ./backend
 RUN go build -o /out/ai-media-hub ./backend
 
+FROM mwader/static-ffmpeg:7.1.1 AS ffmpeg
+
 FROM python:3.12-slim-bookworm
 ENV APP_ROOT=/app \
     PIP_DISABLE_PIP_VERSION_CHECK=1 \
     PYTHONDONTWRITEBYTECODE=1
 WORKDIR /app
 
-RUN apt-get update \
-    && apt-get install -y --no-install-recommends ffmpeg ca-certificates \
-    && rm -rf /var/lib/apt/lists/*
-
 COPY worker/requirements.txt /app/worker/requirements.txt
 RUN python -m pip install --no-cache-dir --upgrade pip \
     && python -m pip install --no-cache-dir -r /app/worker/requirements.txt
 
 COPY --from=go-builder /out/ai-media-hub /app/ai-media-hub
+COPY --from=ffmpeg /ffmpeg /usr/local/bin/ffmpeg
+COPY --from=ffmpeg /ffprobe /usr/local/bin/ffprobe
 COPY worker /app/worker
 COPY frontend /app/frontend
 RUN mkdir -p /app/db /app/downloads