Add detailed logs from the MCP Server

[anannya03]

What does this PR do?

Enable detailed MCP Server logging for live test visibility.

This change allows tests to capture and attach detailed logs without requiring tools like PerfView or dotnet-trace.
Two mechanisms are now supported:

Verbose logging on STDERR – activated via --verbose, or environment variables (AZMCP_LOG_LEVEL, AZMCP_VERBOSE), allowing the test harness to stream logs in real time.

File-based logging – activated via --log-file or AZMCP_LOG_FILE, which writes logs to a specified file for test attachment.

Adds a lightweight SimpleFileLoggerProvider for writing structured logs to disk.
Improves debuggability and reduces friction during live test runs by making server logs directly accessible through the test harness.

GitHub issue number?

#142

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)

[Copilot]

Pull Request Overview

This PR enables detailed MCP Server logging for live test visibility by adding comprehensive logging configuration options. The changes allow tests to capture logs through both verbose stderr output and file-based logging without requiring additional debugging tools.

Key changes:

• Added configurable logging levels and verbose mode through command line options and environment variables
• Implemented file-based logging with placeholder support for timestamps and process IDs
• Enhanced logging configuration for both STDIO and HTTP server modes

Reviewed Changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 2 comments.

File	Description
SimpleFileLoggerProvider.cs	New lightweight file logger implementation for structured log output
ServiceStartOptions.cs	Added logging configuration properties (LogLevel, Verbose, LogFile)
ServiceOptionDefinitions.cs	Defined new command line options for logging controls
ServiceStartCommand.cs	Integrated logging options with environment variable support and enhanced logging setup

Comments suppressed due to low confidence (1)

core/Azure.Mcp.Core/src/Services/Logging/SimpleFileLoggerProvider.cs:1

• The Verbose option should be of type Option instead of Option<string?> since it represents a boolean flag. The DefaultValueFactory should return a boolean value false instead of the string "false".

// Copyright (c) Microsoft Corporation.