Adding public API test coverage for Aspire.NATS.Net

[Alirexaa]

Contributes to #2649 and #5047

Checklist

• Is this feature complete?
  • [X] Yes. Ready to ship.
  • [ ] No. Follow-up changes expected.
• Are you including unit tests for the changes and scenario tests if relevant?
  • [X] 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
  • [X] 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
  • [X] No
• Does the change require an update in our Aspire docs?
  • [ ] Yes
    • Link to aspire-docs issue:
  • [X] No

Microsoft Reviewers: Open in CodeFlow