feat: setup full Next.js toolchain and core dependencies

- Add runtime deps: react-query, react-hook-form+zod, zustand, ky, openapi-fetch,
  better-auth, react-markdown, shiki, recharts, next-themes, nuqs, sonner, cmdk,
  vaul, embla-carousel-react, motion, date-fns, tailwind-merge, clsx, cva
- Add dev tooling: vitest, testing-library, playwright, prettier(+tailwind plugin),
  husky, lint-staged, jsdom
- Wire providers (QueryClient, Theme, NuqsAdapter, Tooltip, Sonner) into layout
- Add vitest/playwright/prettier configs + lint-staged pre-commit hook
- Add lib/query-client + lib/http (ky) helpers and sample unit test
- Fix react-hooks/set-state-in-effect lint errors (use-mobile useSyncExternalStore,
  carousel async init)
- Remove committed Next-generated types/ duplicates (regenerated under .next/types)

.gitignore

@@ -32,6 +32,7 @@ yarn-error.log*
 
 # env files (can opt-in for committing if needed)
 .env*
+!.env.example
 
 # vercel
 .vercel
@@ -39,3 +40,11 @@ yarn-error.log*
 # typescript
 *.tsbuildinfo
 next-env.d.ts
+
+# test tooling
+coverage
+.nyc_output
+test-results
+playwright-report
+blob-report
+.playwright