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)

components.json

@@ -0,0 +1,25 @@
+{
+  "$schema": "https://ui.shadcn.com/schema.json",
+  "style": "base-nova",
+  "rsc": true,
+  "tsx": true,
+  "tailwind": {
+    "config": "",
+    "css": "app/globals.css",
+    "baseColor": "neutral",
+    "cssVariables": true,
+    "prefix": ""
+  },
+  "iconLibrary": "lucide",
+  "rtl": false,
+  "aliases": {
+    "components": "@/components",
+    "utils": "@/lib/utils",
+    "ui": "@/components/ui",
+    "lib": "@/lib",
+    "hooks": "@/hooks"
+  },
+  "menuColor": "default",
+  "menuAccent": "subtle",
+  "registries": {}
+}