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)

app/layout.tsx

@@ -1,6 +1,7 @@
 import type { Metadata } from "next";
 import { Geist, Geist_Mono } from "next/font/google";
 import "./globals.css";
+import { Providers } from "@/components/providers";
 
 const geistSans = Geist({
   variable: "--font-geist-sans",
@@ -22,8 +23,11 @@ export default function RootLayout({ children }: LayoutProps<"/">) {
     <html
       lang="en"
       className={`${geistSans.variable} ${geistMono.variable} h-full antialiased`}
+      suppressHydrationWarning
     >
-      <body className="min-h-full flex flex-col">{children}</body>
+      <body className="flex min-h-full flex-col">
+        <Providers>{children}</Providers>
+      </body>
     </html>
   );
 }