Puppeteer: Chrome Remote Launch
You can start Chromium manually on your host machine and then connect to its WebSocket port using puppeteer.connect() - https://pptr.dev/#?product=Puppeteer&version=v1.8.0&show=api-puppeteerconnectoptions . Don't forgot to open the WS port to container.
We also experimented with running Puppeteer in non-headless mode inside the Docker container using XVFB (X virtual framebuffer) and noVNC (https://github.com/novnc/noVNC) to display whats on the screen at HTML page served from the container. But that's not ideal for debugging.
If you just want to see which pages are opened and their screenshots you could use live-view https://github.com/apifytech/apify-js#puppeteer-live-view we build exactly for this use case.