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/breadcrumb.tsx

@@ -0,0 +1,102 @@
+import * as React from "react";
+import { mergeProps } from "@base-ui/react/merge-props";
+import { useRender } from "@base-ui/react/use-render";
+import { cn } from "cn";
+import { ChevronRightIcon, MoreHorizontalIcon } from "lucide-react";
+
+function Breadcrumb({ className, ...props }: React.ComponentProps<"nav">) {
+  return (
+    <nav aria-label="breadcrumb" data-slot="breadcrumb" className={cn(className)} {...props} />
+  );
+}
+
+function BreadcrumbList({ className, ...props }: React.ComponentProps<"ol">) {
+  return (
+    <ol
+      data-slot="breadcrumb-list"
+      className={cn(
+        "flex flex-wrap items-center gap-1.5 text-sm wrap-break-word text-muted-foreground",
+        className
+      )}
+      {...props}
+    />
+  );
+}
+
+function BreadcrumbItem({ className, ...props }: React.ComponentProps<"li">) {
+  return (
+    <li
+      data-slot="breadcrumb-item"
+      className={cn("inline-flex items-center gap-1", className)}
+      {...props}
+    />
+  );
+}
+
+function BreadcrumbLink({ className, render, ...props }: useRender.ComponentProps<"a">) {
+  return useRender({
+    defaultTagName: "a",
+    props: mergeProps<"a">(
+      {
+        className: cn("transition-colors hover:text-foreground", className),
+      },
+      props
+    ),
+    render,
+    state: {
+      slot: "breadcrumb-link",
+    },
+  });
+}
+
+function BreadcrumbPage({ className, ...props }: React.ComponentProps<"span">) {
+  return (
+    <span
+      data-slot="breadcrumb-page"
+      role="link"
+      aria-disabled="true"
+      aria-current="page"
+      className={cn("font-normal text-foreground", className)}
+      {...props}
+    />
+  );
+}
+
+function BreadcrumbSeparator({ children, className, ...props }: React.ComponentProps<"li">) {
+  return (
+    <li
+      data-slot="breadcrumb-separator"
+      role="presentation"
+      aria-hidden="true"
+      className={cn("[&>svg]:size-3.5", className)}
+      {...props}
+    >
+      {children ?? <ChevronRightIcon />}
+    </li>
+  );
+}
+
+function BreadcrumbEllipsis({ className, ...props }: React.ComponentProps<"span">) {
+  return (
+    <span
+      data-slot="breadcrumb-ellipsis"
+      role="presentation"
+      aria-hidden="true"
+      className={cn("flex size-5 items-center justify-center [&>svg]:size-4", className)}
+      {...props}
+    >
+      <MoreHorizontalIcon />
+      <span className="sr-only">More</span>
+    </span>
+  );
+}
+
+export {
+  Breadcrumb,
+  BreadcrumbList,
+  BreadcrumbItem,
+  BreadcrumbLink,
+  BreadcrumbPage,
+  BreadcrumbSeparator,
+  BreadcrumbEllipsis,
+};