Reuse Event Hubs client for health checks

[sebastienros]

Description

Fixes #7537

Checklist

• Is this feature complete?
  • Yes. Ready to ship.
  • No. Follow-up changes expected.
• Are you including unit tests for the changes and scenario tests if relevant?
  • Yes
  • No
• Did you add public API?
  • Yes
    • If yes, did you have an API Review for it?
      • Yes
      • No
    • Did you add <remarks /> and <code /> elements on your triple slash comments?
      • Yes
      • No
  • No
• Does the change make any security assumptions or guarantees?
  • Yes
    • If yes, have you done a threat model and had a security review?
      • Yes
      • No
  • No
• Does the change require an update in our Aspire docs?
  • Yes
    • Is this introducing a breaking change?
      • Yes
        • Link to aspire-docs issue (please use this breaking-change template):
      • No
        • Link to aspire-docs issue (please use this doc-idea template):
  • No

[Copilot]

Copilot reviewed 6 out of 6 changed files in this pull request and generated no comments.

[sebastienros]

/backport to release/9.1

[github-actions]

Started backporting to release/9.1: https://github.com/dotnet/aspire/actions/runs/13342254632