Add node symlink to Dockerfile; expand ytdlp-test diagnostics

Debian installs nodejs as /usr/bin/nodejs but yt-dlp looks for 'node'.
The symlink ensures yt-dlp can find the runtime.

Diagnostics now report node path/version and yt-dlp version so we can
verify the environment without shelling into the container.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/Dockerfile

@@ -2,7 +2,9 @@ FROM python:3.12-slim
 
 WORKDIR /app
 
-RUN apt-get update && apt-get install -y ffmpeg gosu nodejs && rm -rf /var/lib/apt/lists/*
+RUN apt-get update && apt-get install -y ffmpeg gosu nodejs && \
+    ln -sf /usr/bin/nodejs /usr/bin/node && \
+    rm -rf /var/lib/apt/lists/*
 
 COPY backend/requirements.txt ./backend/requirements.txt
 RUN pip install --no-cache-dir -r backend/requirements.txt && pip install --no-cache-dir -U yt-dlp