Shard name vs. Shard updates, general tech debt cleanup

What does this MR do?

• Fixes a potential time difference race condition
• Increases test coverage
• Explicitly refer to shard names as shard_names where it's a String vs. and actual shard object
• Improve readability of how of healthy_shard_names works

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

N/A

Why was this MR needed?

Technical debt / tidy up

Screenshots (if relevant)

N/A

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
• [ ] EE specific content should be in the top level /ee folder
• Conform by the merge request performance guides
• Conform by the style guides
• Squashed related commits together
• [ ] Internationalization required/considered
• [ ] If paid feature, have we considered GitLab.com plan and how it works for groups and is there a design for promoting it to users who aren't on the correct plan
• End-to-end tests pass (package-qa manual pipeline job)

What are the relevant issue numbers?

Closes #4957 (closed)