.NET: Background responses sample

[markwallace-microsoft]

Motivation and Context

Description

Contribution Checklist

• The code builds clean without any errors or warnings
• The PR follows the Contribution Guidelines
• All unit tests pass, and I have added new tests where possible
• Is this a breaking change? If yes, add "[BREAKING]" prefix to the title of the PR.

[Copilot]

Pull Request Overview

This PR adds a new advanced sample demonstrating background responses with function calling and state persistence. The sample (Agent_Step20_BackgroundResponses_Advanced) builds on the simpler Agent_Step17_BackgroundResponses sample by introducing function tools and state persistence capabilities.

• Demonstrates polling for background responses with function calling
• Shows how to persist and restore agent state (thread and continuation token) between polling cycles
• Includes example functions with simulated long-running operations

Reviewed Changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
dotnet/samples/GettingStarted/Agents/Agent_Step20_BackgroundResponses_Advanced/README.md	Documentation explaining the advanced background responses sample with prerequisites
dotnet/samples/GettingStarted/Agents/Agent_Step20_BackgroundResponses_Advanced/Program.cs	Main sample code demonstrating background responses with state persistence
dotnet/samples/GettingStarted/Agents/Agent_Step20_BackgroundResponses_Advanced/Agent_Step20_BackgroundResponses_Advanced.csproj	Project configuration file
dotnet/samples/GettingStarted/Agents/Agent_Step20_BackgroundResponses_Advanced/AgentStateStore.cs	Helper class for persisting and restoring agent state
dotnet/samples/GettingStarted/Agents/Agent_Step20_BackgroundResponses_Advanced/AgentFunctions.cs	Sample functions for research and character generation
dotnet/agent-framework-dotnet.slnx	Added new sample project to the solution

[rogerbarreto]

Instead of returning an IEnumerable<AIFunction> that could be a IList<AIFunction>.

Suggested change

	tools: [.. new AgentFunctions().AsAITools()]);
	tools: new AgentFunctions().AsAITools());

[rogerbarreto]

Suggested change

	public IEnumerable<AITool> AsAITools()
	{
	yield return AIFunctionFactory.Create(this.ResearchSpaceFactsAsync);
	yield return AIFunctionFactory.Create(this.GenerateCharacterProfilesAsync);
	}
	public IList<AITool> AsAITools() =>
	[
	AIFunctionFactory.Create(this.ResearchSpaceFactsAsync),
	AIFunctionFactory.Create(this.GenerateCharacterProfilesAsync)
	];