docker：Cannot connect to the Docker daemon at unix:///var/run/docker.sock. Is the docker daemon running?

I'm remotely connecting to a school server (Ubuntu 20.04.2 LTS) through Visual Studio Code (VScode, version 1.66) to perform some tasks, and today I follow docker.com (https://docs.docker.com/engine/install/ubuntu/) to install docker engine on Ubuntu.

when I do sudo docker run hello-world to verify that Docker Engine is installed correctly by running the hello-world image after all steps, it shows error like this:

docker: Cannot connect to the Docker daemon at unix:///var/run/docker.sock. Is the docker daemon running?.See 'docker run --help'.

After that I check the docker version, it shows

Client: Docker Engine - Community Version: 20.10.14 API version: 1.41 Go version: go1.16.15 Git commit: a224086 Built: Thu Mar 24 01:48:02 2022 OS/Arch: linux/amd64 Context: default Experimental: trueCannot connect to the Docker daemon at unix:///var/run/docker.sock. Is the docker daemon running?

Then look at sudo docker info, which shows

Client: Context: default Debug Mode: false Plugins:  app: Docker App (Docker Inc., v0.9.1-beta3)  buildx: Docker Buildx (Docker Inc., v0.8.1-docker)  scan: Docker Scan (Docker Inc., v0.17.0)Server:ERROR: Cannot connect to the Docker daemon at unix:///var/run/docker.sock. Is the docker daemon running?errors pretty printing info

After I unstall and reinstall docker follow this tutorial, it still shows such an error, I think I need to follow the server side of docker, but I don't know how to do it?

This is history:

root@yp:~# sudo apt-get remove docker docker-engine docker.io containerd runc...root@yp:~# sudo apt-get update...root@yp:~# sudo apt-get install \>     ca-certificates \>     curl \>     gnupg \>     lsb-release...root@yp:~# curl -fsSL https://download.docker.com/linux/ubuntu/gpg | sudo gpg --dearmor -o /usr/share/keyrings/docker-archive-keyring.gpg...root@yp:~# echo \>   "deb [arch=$(dpkg --print-architecture) signed-by=/usr/share/keyrings/docker-archive-keyring.gpg] https://download.docker.com/linux/ubuntu \>   $(lsb_release -cs) stable" | sudo tee /etc/apt/sources.list.d/docker.list > /dev/null...root@yp:~# sudo apt-get update...root@yp:~# sudo apt-get install docker-ce docker-ce-cli containerd.io...root@yp:~# sudo docker run hello-worlddocker: Cannot connect to the Docker daemon at unix:///var/run/docker.sock. Is the docker daemon running?.See 'docker run --help'.