Add Docker to list of docs engineering-managed tools

What does this MR do and why?

To provide more coverage of all dependencies declared in the project, add Docker versions as a docs engineering-managed dependency.

Also roll the version of Docker used in the project forward.

Jobs that use new version of Docker-in-Docker:

• https://gitlab.com/gitlab-org/technical-writing/docs-gitlab-com/-/jobs/11529752653
• https://gitlab.com/gitlab-org/technical-writing/docs-gitlab-com/-/jobs/11529752651

Merge request acceptance checklist

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• I have evaluated the MR acceptance checklist for this merge request.