DI Refactor: Azure.Mcp.Tools.AppService

[conniey]

Summary

Refactor Azure.Mcp.Tools.AppService to use constructor dependency injection instead of resolving services via context.GetService<T>() in ExecuteAsync.

This is a sub-issue of #158.

Instructions

Follow the algorithm described in tools/di-refactor-plan.md with {ToolArea} = AppService.

An example PR is: #1815

[github-actions]

Thanks for the feedback! We are routing this to the appropriate team for follow-up. cc @ArthurMa1978 @KarishmaGhiya @weidongxu-microsoft.