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)

hooks/use-mobile.ts

@@ -0,0 +1,17 @@
+import * as React from "react";
+
+const MOBILE_BREAKPOINT = 768;
+
+export function useIsMobile() {
+  const subscribe = React.useCallback((callback: () => void) => {
+    const mql = window.matchMedia(`(max-width: ${MOBILE_BREAKPOINT - 1}px)`);
+    mql.addEventListener("change", callback);
+    return () => mql.removeEventListener("change", callback);
+  }, []);
+
+  const getSnapshot = React.useCallback(() => window.innerWidth < MOBILE_BREAKPOINT, []);
+
+  const getServerSnapshot = React.useCallback(() => false, []);
+
+  return React.useSyncExternalStore(subscribe, getSnapshot, getServerSnapshot);
+}