Add C# GroupChat tool approval sample for multi-agent orchestrations

[Copilot]

Motivation and Context

Adds C# equivalent of the Python group_chat_builder_tool_approval.py sample to demonstrate human-in-the-loop approvals within multi-agent workflows.

Description

Implements a deployment workflow where QA and DevOps agents collaborate, with production deployment requiring human approval.

Implementation:

• Program.cs - Two-phase workflow: run until approval needed, handle approval, resume
• DeploymentGroupChatManager.cs - Custom speaker selection extending GroupChatManager using agent Name property for selection
• Tools defined with ApprovalRequiredAIFunction wrapper for sensitive operations
• Event handling for FunctionApprovalRequestContent during workflow execution
• Solution Integration: Added project to agent-framework-dotnet.slnx solution file in /Samples/GettingStarted/Workflows/Agents/ folder
• File Encoding: All C# source files use UTF-8 with BOM encoding as required by the repository's formatter

Key patterns demonstrated:

// Approval-required tool
new ApprovalRequiredAIFunction(AIFunctionFactory.Create(DeployToProduction))

// Custom speaker selection using agent Name property
protected override ValueTask<AIAgent> SelectNextAgentAsync(
    IReadOnlyList<ChatMessage> history, CancellationToken cancellationToken)
{
    AIAgent agent = this._agents.First(a => a.Name == "QAEngineer");
    return new ValueTask<AIAgent>(agent);
}

// Approval handling
FunctionApprovalRequestContent? approvalRequest = e.Update.Contents
    .OfType<FunctionApprovalRequestContent>()
    .FirstOrDefault();

Technical notes:

• Override methods in GroupChatManager subclasses from external assemblies must use protected (not protected internal)
• Tools passed via ChatClientAgent constructor, not as settable properties
• Agent selection uses the Name property (set during agent creation) rather than the auto-generated Id property
• C# source files must use UTF-8 encoding with BOM to comply with the repository's code formatter requirements

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.

Original prompt

---

This section details on the original issue you should resolve

<issue_title>E2E sample of agent approvals in multi-agent orchestrations</issue_title>
<issue_description>The outcome of this task is that we have a test or sample of agent approvals being used within a multi-agent orchestration.

There is an AIAgent Executor which will be used for multi-agent orchestration so you should collaborate with respective owners of .Net and Python implementations.</issue_description>

<agent_instructions>Add a C# sample that is equivalent to this Python sample - https://github.com/microsoft/agent-framework/blob/main/python/samples/getting_started/workflows/tool-approval/group_chat_builder_tool_approval.py.</agent_instructions>

Comments on the Issue (you are @copilot in this section)

@dmytrostruk Python sample: https://github.com/microsoft/agent-framework/blob/main/python/samples/getting_started/workflows/tool-approval/group_chat_builder_tool_approval.py

• Fixes E2E sample of agent approvals in multi-agent orchestrations #447

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[SergeyMenshykh]

@copilot add this project to the solution

[Copilot]

@copilot add this project to the solution

Added to the solution in commit 237e5a6. The GroupChatToolApproval project is now included in the /Samples/GettingStarted/Workflows/Agents/ folder in alphabetical order.

[SergeyMenshykh]

@copilot dotnet build failed with the errors:
Running formatters.
/app/dotnet/samples/GettingStarted/Workflows/Agents/GroupChatToolApproval/DeploymentGroupChatManager.cs(1,1): error CHARSET: Fix file encoding. [/app/dotnet/samples/GettingStarted/Workflows/Agents/GroupChatToolApproval/GroupChatToolApproval.csproj]
/app/dotnet/samples/GettingStarted/Workflows/Agents/GroupChatToolApproval/Program.cs(1,1): error CHARSET: Fix file encoding. [/app/dotnet/samples/GettingStarted/Workflows/Agents/GroupChatToolApproval/GroupChatToolApproval.csproj]