.NET: Use Responses API for hosted web search in AG-UI

[Copilot]

Motivation & Context

HostedWebSearchTool uses web_search_options with Chat Completions. Azure OpenAI deployments can reject that parameter with HTTP 400. The AG-UI server sample needs the Responses API wire format, where web search appears in the tools array.

Description & Review Guide

• What are the major changes? The AG-UI server now uses the OpenAI SDK directly with BearerTokenPolicy and a Responses client. The sample no longer depends on Azure.AI.OpenAI. Documentation now explains the Azure OpenAI v1 endpoint and distinguishes direct inference from a Foundry project. Unit coverage captures the outbound request and confirms tools[].type is web_search while web_search_options is absent.
• What is the impact of these changes? Hosted web search uses the Azure OpenAI Responses API wire format and avoids the unsupported parameter reported in issue .NET: [Bug]: Request processing fails when web search is enabled because of an unsupported web_search_options parameter #7578.
• What do you want reviewers to focus on? Review the direct OpenAI SDK authentication, Responses client selection, and outbound request shape.

IChatClient chatClient = new OpenAIClient(
        new BearerTokenPolicy(new DefaultAzureCredential(), "https://ai.azure.com/.default"),
        new OpenAIClientOptions { Endpoint = new Uri(endpoint) })
    .GetResponsesClient()
    .AsIChatClient(deploymentName);

Related Issue

Fixes #7578

Contribution Checklist

• The code builds clean without any errors or warnings
• All unit tests pass, and I have added new tests where possible
• The PR follows the Contribution Guidelines
• This PR is linked to an issue and there is no other open PR for this issue (see Related Issue above).
• This is not a breaking change.

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[Roger Barreto (rogerbarreto)]

/review

[github-actions]

MAF Automated Review — Iteration 1

Result: Findings reported
Scope: full PR (4 commit(s)): c0a5259a3ec2, 011496904bb2, 3f197c8c812a, 9dfa3afdfcc9
Model: gpt-5.6-sol

Overview

The PR correctly moves hosted web search to the Responses API, and the new transport-level test verifies the /v1/responses route and web_search tool shape while excluding the unsupported Chat Completions parameter. The Azure endpoint and bearer-token setup are documented clearly. However, the default stored-output Responses client makes the sample's session continuity depend on service-side response retention rather than the configured session store.

Reviewed the supplied pull-request change set across correctness, security/reliability, architecture, and failure behavior.
1 verified finding remained after source verification (1 medium) across 1 file. Details are attached to the affected lines below.

Affected areas: dotnet/samples/05-end-to-end/AGUIClientServer/AGUIServer/Program.cs