There's a ~/.docker/config.json. In that there're some auths, with keys https://index.docker.io/v1/, https://index.docker.io/v1/access-token, and https://index.docker.io/v1/refresh-token, and then there's "currentContext": "rootless".
There's ~/.docker/contexts/meta/[a long hex string]/meta.json, with {"Name":"rootless","Metadata":{"Description":"Rootless mode"},"Endpoints":{"docker":{"Host":"unix:///run/user/1000/docker.sock","SkipTLSVerify":false}}}.
The only file in /etc/docker is key.json.