[ENH] Vite Stack

[b-jonathan]

Is your feature request related to a problem?
I want to be able to make a Vite app

Describe the solution
Add Vite with React + TypeScript as a new frontend option alongside Next.js.

Requirements:

• Scaffold using create-vite with the react-ts template
• Include Tailwind CSS setup (matching the Next.js stack's styling approach)
• Include React Router — install react-router and scaffold a basic route structure with sample pages
• Add ESLint + Prettier config (same pattern as Next.js: eslint, typescript-eslint,
  eslint-config-prettier, prettier)
• Generate .env with VITE_BACKEND_URL=http://localhost:4000
• Add lint scripts (lint-check, lint-fix) to package.json via nodepkg.InitPackage
• Add templates under vite/ in the embedded template directory
• Firebase auth compatibility: add firebase/vite/ templates if firebase should work with Vite (or
  scope firebase to Next.js only for now)
• Register as "vite" in the stack registry