docker-proxy remain running after unit stopped

Description

Failed to start as the docker-proxy cannot closed.

Reproduce

1. Error: bash: usr/bin/docker: Permission denied
2. change permission: chmod 666 /usr/bin/docker
3. Added SupplementaryGroups=docker
   ExecStartPost=/bin/chmod 666 /var/run/docker.sock
4. sudo systemctl status docker

Expected behavior

No response

docker version

version:20.10.21

docker info

unable to show

Additional Info

ii docker-ce 5:20.10.213-0ubuntu-jammy amd64 Docker: the open-source application container engine
ii docker-ce-cli 5:20.10.213-0ubuntu-jammy amd64 Docker CLI: the open-source application container engine
ii docker-ce-rootless-extras 5:20.10.213-0ubuntu-jammy amd64 Rootless support for Docker.
ii docker-compose-plugin 2.12.2ubuntu-jammy amd64 Docker Compose (V2) plugin for the Docker CLI.
ii docker-scan-plugin 0.21.0ubuntu-jammy amd64 Docker scan cli plugin.

Start by reviewing the reported reproduction steps, the Docker 20.10.21 package details, and the sudo systemctl status docker output described in the issue. Reproduce the service stop and startup failure, then verify that docker-proxy no longer remains running after the unit stops and that Docker can start successfully.