I'm guessing this is done through code-server?

correct

I'm currently rolling a JupyterHub instance (multiuser, with codeserver inside) on the same machine as clearml-server. That’s where tasks are executed etc. so, all browser dev env.

Yeah, the idea with clearml-session each user can self serve themselves the container that works best for them. With a jupyterhub they start to step on each other's toes very quickly ...