Migrate to new generatequery API endpoint

[JasonYeMSFT]

For the LLM tool in VS Code extension.

[github-actions]

Thanks for opening this issue, @JasonYeMSFT! 🙌

This has been labeled as an enhancement since it involves migrating to a new API endpoint, and tagged with vscode given it targets the VS Code extension's LLM tool. A coding agent has been assigned via assign-to-copilot to help with the implementation work for this migration.

Generated by Issue Triage for issue #1090