I meant, for the runner to be in Kubernetes as a docker. And from that runner to run docker commands. Basically not to have a virtual machine, but only a docker runner from which I would do everything. Something similar as there is in GitLab with their runners, to have the runner, and then I just specify the image (node:latest for example), i do all the which I want to use for the specific build. So I do all my actions in the docker, code is pulled in the docker itself I do the whole docker build, docker push commands.
But as you stated, for docker commands to run I would need docker installed inside of that docker (so i need to bring the runner in a docker image with docker already installed), or for Container actions it needs to be the Linux machine with docker installed on it.
My idea was to not have a separate server just for the runner service, but to use K8s cluster and use dockers to the build and deploy. To put it in the most easy way possible