Passes Environment into New-TestSettings, Simplifies Configuration

[conniey]

What does this PR do?

• Passes $Environment into test scripts and test-settings to be used by live tests.
• Simplifies search for configuration lookup in AzureCloudConfiguration.
• Removes Azure.Mcp.Server.LiveTests -> The tests have already been absorbed into Azure.Mcp.Core.LiveTests in main. (somehow changes were not reflected here)

Sample build: https://dev.azure.com/azure-sdk/internal/_build/results?buildId=6127336&view=results

GitHub issue number?

[Link to the GitHub issue this PR addresses]

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
  • Created a changelog entry if the change falls among the following: new feature, bug fix, UI/UX update, breaking change, or updated dependencies. Follow the changelog entry guide
• 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 running the script ./eng/scripts/Process-PackageReadMe.ps1. See Package README
  • 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 renamed tools, follow the Tool Rename Checklist and tag the PR with the breaking-change label
  • 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 command list in servers/Azure.Mcp.Server/docs/azmcp-commands.md
  • Ran ./eng/scripts/Update-AzCommandsMetadata.ps1 to update tool metadata in azmcp-commands.md (required for CI)
  • 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

[jongio]

tools/Azure.Mcp.Tools.DeviceRegistry/tests/test-resources-post.ps1 exists on the base branch but wasn't updated with the $Environment parameter. 41 of 42 test-resources-post.ps1 files got the new parameter - looks like DeviceRegistry was missed.

[jongio]

Environment propagation through the test pipeline is correct. The AzureCloudConfiguration simplification is valid - IConfiguration keys are case-insensitive, so the duplicated lookups were unnecessary. Server.LiveTests removal is clean since those tests already exist in Core.LiveTests.

No new issues beyond what's already in review.