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/input.tsx

@@ -0,0 +1,19 @@
+import * as React from "react";
+import { Input as InputPrimitive } from "@base-ui/react/input";
+import { cn } from "cn";
+
+function Input({ className, type, ...props }: React.ComponentProps<"input">) {
+  return (
+    <InputPrimitive
+      type={type}
+      data-slot="input"
+      className={cn(
+        "h-8 w-full min-w-0 rounded-lg border border-input bg-transparent px-2.5 py-1 text-base transition-colors outline-none file:inline-flex file:h-6 file:border-0 file:bg-transparent file:text-sm file:font-medium file:text-foreground placeholder:text-muted-foreground focus-visible:border-ring focus-visible:ring-3 focus-visible:ring-ring/50 disabled:pointer-events-none disabled:cursor-not-allowed disabled:bg-input/50 disabled:opacity-50 aria-invalid:border-destructive aria-invalid:ring-3 ariLine truncated
+        className
+      )}
+      {...props}
+    />
+  );
+}
+
+export { Input };