Remove deprecated AzureAIAgentsPersistent sample

Remove the deprecated providers/azure/Agent_With_AzureAIAgentsPersistent sample and clean up solution and providers index references.\n\nCo-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Author: alliscode

dotnet/agent-framework-dotnet.slnx

@@ -24,7 +24,6 @@
     <File Path="samples/02-agents/providers/README.md" />
     <Project Path="samples/02-agents/providers/a2a/Agent_With_A2A/Agent_With_A2A.csproj" />
     <Project Path="samples/02-agents/providers/anthropic/Agent_With_Anthropic/Agent_With_Anthropic.csproj" />
-    <Project Path="samples/02-agents/providers/azure/Agent_With_AzureAIAgentsPersistent/Agent_With_AzureAIAgentsPersistent.csproj" />
     <Project Path="samples/02-agents/providers/azure/Agent_With_AzureAIProject/Agent_With_AzureAIProject.csproj" />
     <Project Path="samples/02-agents/providers/azure/Agent_With_AzureFoundryModel/Agent_With_AzureFoundryModel.csproj" />
     <Project Path="samples/02-agents/providers/azure/Agent_With_AzureOpenAIChatCompletion/Agent_With_AzureOpenAIChatCompletion.csproj" />

dotnet/samples/02-agents/providers/README.md

@@ -33,7 +33,6 @@ See the README.md for each sample for the prerequisites for that sample.
 
 | Sample | Description |
 | --- | --- |
-| [Azure AI Agents Persistent](./azure/Agent_With_AzureAIAgentsPersistent/) | Create a Foundry Persistent agent using the Azure.AI.Agents.Persistent SDK |
 | [Azure AI Project](./azure/Agent_With_AzureAIProject/) | Create a Foundry Project agent using the Azure.AI.Project SDK |
 | [Azure Foundry Model](./azure/Agent_With_AzureFoundryModel/) | Use any model deployed to Microsoft Foundry |
 | [Azure OpenAI ChatCompletion](./azure/Agent_With_AzureOpenAIChatCompletion/) | Create an AIAgent using Azure OpenAI ChatCompletion |