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/ui/spinner.tsx

@@ -0,0 +1,16 @@
+import { cn } from "cn";
+import { Loader2Icon } from "lucide-react";
+
+function Spinner({ className, ...props }: React.ComponentProps<"svg">) {
+  return (
+    <Loader2Icon
+      data-slot="spinner"
+      role="status"
+      aria-label="Loading"
+      className={cn("size-4 animate-spin", className)}
+      {...props}
+    />
+  );
+}
+
+export { Spinner };