CI: script around docker:dind slow start

What does this MR do?

CI: script around docker:dind slow start

Script around the slow-start of docker:dind, when we only care about the client anyways.

Related issues

https://gitlab.com/gitlab-org/charts/gitlab/-/jobs/5764281519#L87, and many other instances of this error. Started sometime in 2023-12-15 UTC.

Related to #5184 (closed).

Author checklist

See Definition of done.

For anything in this list which will not be completed, please provide a reason in the MR discussion.

Required

• Merge Request Title and Description are up to date, accurate, and descriptive
• MR targeting the appropriate branch
• MR has a green pipeline on GitLab.com
• When ready for review, follow the instructions in the "Reviewer Roulette" section of the Danger Bot MR comment, as per the Distribution experimental MR workflow

Expected (please provide an explanation if not completing)

• Test plan indicating conditions for success has been posted and passes
• Documentation created/updated
• Tests added/updated
• Integration tests added to GitLab QA
• Equivalent MR/issue for omnibus-gitlab opened
• Equivalent MR/issue for Gitlab Operator project opened (see Operator documentation on impact of Charts changes)
• Validate potential values for new configuration settings. Formats such as integer 10, duration 10s, URI scheme://user:passwd@host:port may require quotation or other special handling when rendered in a template and written to a configuration file.