feat: add Deploy MCP App (#10263)

* feat: add Deploy MCP App

Adds the Deploy MCP App UI and resources. Also includes a small fix for firestore deploy to avoid errors on empty indexes.

- Verified build and file changes.

* fix: resolve lint warnings and fix build for deploy app on mcp-deploy-app

* fix: remove unused variables in deploy_ui.ts

* refactor: enhance deploy tracking layout and fix logging duplicate loops

* fix: sync shrinkwrap and lock configs to resolve vs-code testing pipeline regression

Author: joehan