fix: recommend AIProjectClient instead of PersistentAgentsClient

[XiaofuHuang]

What does this PR do?

In the latest release of Microsoft Agent Framework, agent hosted in Azure AI Foundry use AIProjectClient instead of PersistentAgentsClient.

Detail: https://github.com/microsoft/agent-framework/releases/tag/dotnet-1.0.0-preview.251114.1

Pre-merge Checklist

• Required for All PRs
  • Read contribution guidelines
  • PR title clearly describes the change
  • Commit history is clean with descriptive messages (cleanup guide)
  • Added comprehensive tests for new/modified functionality
  • Updated servers/Azure.Mcp.Server/CHANGELOG.md and/or servers/Fabric.Mcp.Server/CHANGELOG.md for product changes (features, bug fixes, UI/UX, updated dependencies)
• For MCP tool changes:
  • One tool per PR: This PR adds or modifies only one MCP tool for faster review cycles
  • Updated servers/Azure.Mcp.Server/README.md and/or servers/Fabric.Mcp.Server/README.md documentation
  • Validate README.md changes using script at eng/scripts/Process-PackageReadMe.ps1. See Package README
  • Updated command list in /servers/Azure.Mcp.Server/docs/azmcp-commands.md and/or /docs/fabric-commands.md
  • Run .\eng\scripts\Update-AzCommandsMetadata.ps1 to update tool metadata in azmcp-commands.md (required for CI)
  • For new or modified tool descriptions, ran ToolDescriptionEvaluator and obtained a score of 0.4 or more and a top 3 ranking for all related test prompts
  • For tools with new names, including new tools or renamed tools, update consolidated-tools.json
  • For new tools associated with Azure services or publicly available tools/APIs/products, add URL to documentation in the PR description
• Extra steps for Azure MCP Server tool changes:
  • Updated test prompts in /servers/Azure.Mcp.Server/docs/e2eTestPrompts.md
  • 👉 For Community (non-Microsoft team member) PRs:
    • Security review: Reviewed code for security vulnerabilities, malicious code, or suspicious activities before running tests (crypto mining, spam, data exfiltration, etc.)
    • Manual tests run: added comment /azp run mcp - pullrequest - live to run Live Test Pipeline

[XiaofuHuang]

/azp run mcp - pullrequest - live

[azure-pipelines]

Azure Pipelines successfully started running 1 pipeline(s).

[Copilot]

Pull Request Overview

This PR updates the Azure AI Best Practices documentation to recommend AIProjectClient instead of the legacy PersistentAgentsClient for creating agents in Azure AI Foundry. This aligns with the latest Microsoft Agent Framework release (dotnet-1.0.0-preview.251114.1).

Key changes:

• Updated agent type recommendations from PersistentAgentsClient to AIProjectClient across all documentation files
• Added new code examples demonstrating AIProjectClient usage patterns
• Marked PersistentAgentsClient as legacy with migration guidance
• Updated package installation instructions to clarify that Azure.AI.Projects is included transitively

Reviewed Changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 7 comments.

File	Description
tools/Azure.Mcp.Tools.AzureAIBestPractices/src/Resources/ai-error-patterns.txt	Replaced PersistentAgentsClient examples with AIProjectClient patterns, including comprehensive code samples for creating agents with tools and structured output
tools/Azure.Mcp.Tools.AzureAIBestPractices/src/Resources/ai-best-practices-core.txt	Updated SDK selection guidance and installation instructions to recommend AIProjectClient, changed quickstart reference to GitHub sample
tools/Azure.Mcp.Tools.AzureAIBestPractices/src/Resources/ai-background-knowledge.txt	Updated agent types documentation to list AIProjectClient as recommended and PersistentAgentsClient as legacy