Following the idea of https://github.com/machulav/ec2-github-runner to start an "on demand" GitHub actions runner at Hetzner I found that this action can be configured to not delete the instance after the (setup) job has run. But in the end, one needs to clean up the instance.
It would be great if there would be an "out of the box" solution for this, similar to this "deploy-server-action".