[azsdk-cli] Investigate vscode extension installer for azsdk mcp

Installing our mcp server by packaging it as a vscode extension may be an easy way for new users to install it without having to worry about mcp config files, sync scripts, etc. especially for partner service teams that may not even have the repo set up.

FYI @scbedd @praveenkuttappan @maririos

Review the azsdk-cli MCP server installation flow and the requirements for packaging it as a VS Code extension. Determine whether the extension can remove the need for MCP config files and sync scripts for partner service teams, and document the feasibility and recommended next steps.

Written by the indexing model from the issue text.