chore(web): scaffold Next.js web application with TypeScript, Tailwind CSS, and shadcn/ui #4

Summary

Initialize the ProblemSpot Next.js web application according to the architectural layout defined in docs/ARCHITECTURE.md (Section 4).

Scope

• Initialize Next.js (App Router) with TypeScript.
• Set up Tailwind CSS with brand colors from brand.md (brand-green: #168447, brand-blue: #2563EB, etc.).
• Set up shadcn/ui component base.
• Structure directories:
  • app/ ((public), (auth), dashboard/, admin/, api/)
  • components/
  • features/
  • lib/
  • tests/
• Add root package.json, tsconfig.json, .env.example, ESLint, and Prettier configurations.

Acceptance Criteria

• Next.js application boots without errors on npm run dev.
• Static type check passes with 0 errors (tsc --noEmit).
• Brand tokens from brand.md integrated into Tailwind configuration.