Improve fix for intermittent QA failure in "cloning code using a deploy key"

What does this MR do?

Improve fix for intermittent QA failure in "cloning code using a deploy key".

Are there points in the code the reviewer needs to double check?

Why was this MR needed?

https://gitlab.com/charts/gitlab/issues/396#note_70507289

Screenshots (if relevant)

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• API support added
• Tests added for this feature/bug
• Review
  • Has been reviewed by UX
  • Has been reviewed by Frontend
  • Has been reviewed by Backend
  • Has been reviewed by Database
• Conform by the merge request performance guides
• Conform by the style guides
• Squashed related commits together
• Internationalization required/considered
• End-to-end tests pass (package-and-qa manual pipeline job)

What are the relevant issue numbers?

Resolves https://gitlab.com/charts/gitlab/issues/396#note_70507289