This is applicable from debian bullseye and use docker-ce packages.
$ sudo apt install docker-ce-rootless-extras fuse-overlayfs
$ echo "options overlay permit_mounts_in_userns=1" | sudo tee /etc/modprobe.d/overlay2.conf
$ sudo systemctl disable --now docker.service docker.socket
$ mkdir ~/.config/docker
$ echo '{"storage-driver": "fuse-overlayfs"}' > ~/.config/docker/daemon.json
$ dockerd-rootless-setuptool.sh check
$ dockerd-rootless-setuptool.sh install
$ export DOCKER_HOST=unix:///run/user/$UID/docker.sock
$ docker info