Example of Codespaces running docker-in-docker from the temp disk
The devcontainer (.devcontainer/devcontainer.json) is a minimal Ubuntu 22.04 image with the docker-in-docker feature added in. In the Dockerfile, docker's /etc/docker/daemon.json is configured to set the data-root to be /tmp/docker so that the daemon uses /tmp/docker instead of /var/lib/docker for images/containers/etc.
In Codespaces, the /tmp folder is bind-mounted to a local-attached SSD which has higher IOPS and throughput than the persistent volume, but the tradeoff is that it's ephemeral and gets wiped on restarts. For this sample repo, that means every time you restart your codespace, the docker images and containers start from a clean slate and do not persist.