You can run containers on exozyme using Podman, which is basically Docker but better. Alternatively, you can use Distrobox if you would like an easier, automated way to create and manage containers. If you aren't familiar with containers, first read this intro.
Run containers when logged out
By default, containers won't run when logged out. This is due to users only having access to rootless podman.
To fix this, run loginctl enable-linger $USER. This makes systemd run your services (including podman) even if you logged out.