Update Azure Cognitive Search to Azure AI Search in chat template documentation (dotnet#47325)

* Initial plan

* Update Azure Cognitive Search to Azure AI Search in chat template doc

Co-authored-by: gewarren <24882762+gewarren@users.noreply.github.com>

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Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: gewarren <24882762+gewarren@users.noreply.github.com>

Author: Copilot

docs/ai/get-started-app-chat-template.md

@@ -39,7 +39,7 @@ The architecture of the chat app is shown in the following diagram:
 
 - **User interface** - The application's chat interface is a [Blazor WebAssembly](/aspnet/core/blazor/) application. This interface is what accepts user queries, routes request to the application backend, and displays generated responses.
 - **Backend** - The application backend is an [ASP.NET Core Minimal API](/aspnet/core/fundamentals/minimal-apis/overview). The backend hosts the Blazor static web application and is what orchestrates the interactions among the different services. Services used in this application include:
-  - [**Azure Cognitive Search**](/azure/search/search-what-is-azure-search) – Indexes documents from the data stored in an Azure Storage Account. This makes the documents searchable using [vector search](/azure/search/search-get-started-vector) capabilities.
+  - [**Azure AI Search**](/azure/search/search-what-is-azure-search) – Indexes documents from the data stored in an Azure Storage Account. This makes the documents searchable using [vector search](/azure/search/search-get-started-vector) capabilities.
   - [**Azure OpenAI Service**](/azure/ai-services/openai/overview) – Provides the Large Language Models (LLM) to generate responses. [Semantic Kernel](/semantic-kernel/whatissk) is used in conjunction with the Azure OpenAI Service to orchestrate the more complex AI workflows.
 
 ## Cost