Current Docker context not used when connected to SSH server

• VSCode Version: 1.63.2
• Local OS Version: Windows 11
• Remote OS Version: Ubuntu 20.04
• Remote Extension/Connection Type: Remote SSH + Remote Containers
• Logs:
  [14769 ms] Remote-Containers 0.209.6 in VS Code 1.63.2 (899d46d82c4c95423fb7e10e68eba52050e30ba3).
  [14769 ms] Start: Run: ssh 10.0.62.168 /bin/sh -c /bin/sh
  [14784 ms] Start: Run in host: id -un
  [15100 ms] patel_zeel
  [15100 ms]
  [15101 ms] Start: Run in host: cat /etc/passwd
  [15106 ms] Start: Run in host: echo ~
  [15111 ms] /home/patel_zeel
  [15111 ms]
  [15112 ms] Start: Run in host: test -x '/home/patel_zeel/.vscode-remote-containers/bin/899d46d82c4c95423fb7e10e68eba52050e30ba3/node'
  [15116 ms]
  [15116 ms]
  [15116 ms] Exit code 1
  [15117 ms] Start: Run in host: test -x '/home/patel_zeel/.vscode-server/bin/899d46d82c4c95423fb7e10e68eba52050e30ba3/node'
  [15120 ms]
  [15121 ms]
  [15121 ms] Start: Run in host: test -f '/home/patel_zeel/.vscode-server/bin/899d46d82c4c95423fb7e10e68eba52050e30ba3/node_modules/node-pty/package.json'
  [15124 ms]
  [15125 ms]
  [15125 ms] Start: Run in host: test -f '/home/patel_zeel/.vscode-remote-containers/dist/vscode-remote-containers-server-0.209.6.js'
  [15131 ms]
  [15131 ms]
  [15135 ms] userEnvProbe: loginInteractiveShell (default)
  [15135 ms] userEnvProbe shell: /bin/bash
  [17145 ms] Start: Run in Host: /bin/sh
  [17155 ms] Start: Run in container: for pid in cd /proc && ls -d [0-9]*; do { echo $pid ; readlink /proc/$pid/cwd ; readlink /proc/$pid/ns/mnt ; cat /proc/$pid/stat | tr "
  [21595 ms] userEnvProbe is taking longer than 2 seconds. Process tree:
  397624: /bin/bash -lic '/home/patel_zeel/.vscode-server/bin/899d46d82c4c95423fb7e10e68eba52050e30ba3/node' -p '"b1c1586b5db1908f0d9c56651a18942c" + JSON.stringify(process.env) + "b1c1586b5db1908f0d9c56651a18942c"'
  397640: zsh
  [25146 ms] userEnvProbe is taking longer than 10 seconds. Avoid waiting for user input in your shell's startup scripts. Continuing.
  [25151 ms] Start: Run in Host: docker version --format {{.Server.APIVersion}}
  [25202 ms]
  [25202 ms] Cannot connect to the Docker daemon at unix:///var/run/docker.sock. Is the docker daemon running?

Steps to Reproduce:

1. Setup rootless docker on a remote machine
2. Connect to the remote machine with Remote-SSH
3. Try to do: Remote-containers: Reopen in Container.

Docker rootless mode is working fine on the remote machine. I have a strong feeling that I just need to set the correct path of docker.sock (unix:///run/uid/docker.sock) instead of current: unix:///var/run/docker.sock. I am unable to figure out a way to do that.