Rewrote the .NET Aspire Azure AI Search doc (#2766)

* Fixes #2315.

* A few minor edits

* Edit pass

* Fix links

* Add missing include bits

* Apply suggestions from code review

Co-authored-by: Andy (Steve) De George <[email protected]>

* Update Azure AI Search connection instructions

* Address peer feedback

---------

Co-authored-by: Andy (Steve) De George <[email protected]>

Author: IEvangelist