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)

lib/query-client.ts

@@ -0,0 +1,28 @@
+import { isServer, QueryClient } from "@tanstack/react-query";
+
+function makeQueryClient() {
+  return new QueryClient({
+    defaultOptions: {
+      queries: {
+        staleTime: 60 * 1000,
+        gcTime: 5 * 60 * 1000,
+        refetchOnWindowFocus: false,
+        retry: 1,
+      },
+    },
+  });
+}
+
+let browserQueryClient: QueryClient | undefined = undefined;
+
+export function getQueryClient() {
+  if (isServer) {
+    // Server: fresh client per request so caches never leak between users.
+    return makeQueryClient();
+  }
+  // Browser: single shared client so the cache survives route changes.
+  if (!browserQueryClient) {
+    browserQueryClient = makeQueryClient();
+  }
+  return browserQueryClient;
+}