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/button.tsx

@@ -0,0 +1,57 @@
+import { Button as ButtonPrimitive } from "@base-ui/react/button";
+import { cva, type VariantProps } from "class-variance-authority";
+import { cn } from "cn";
+
+const buttonVariants = cva(
+  "group/button inline-flex shrink-0 items-center justify-center rounded-lg border border-transparent bg-clip-padding text-sm font-medium whitespace-nowrap transition-all outline-none select-none focus-visible:border-ring focus-visible:ring-3 focus-visible:ring-ring/50 active:not-aria-[haspopup]:translate-y-px disabled:pointer-events-none disabled:opacity-50 aria-invalid:border-destructive aria-invalid:ring-3 aria-invalid:ring-destructive/20 dark:aria-invalid:border-destructive/50 dark:aria-invLine truncated
+  {
+    variants: {
+      variant: {
+        default: "bg-primary text-primary-foreground hover:bg-primary/80",
+        outline:
+          "border-border bg-background hover:bg-muted hover:text-foreground aria-expanded:bg-muted aria-expanded:text-foreground dark:border-input dark:bg-input/30 dark:hover:bg-input/50",
+        secondary:
+          "bg-secondary text-secondary-foreground hover:bg-[color-mix(in_oklch,var(--secondary),var(--foreground)_5%)] aria-expanded:bg-secondary aria-expanded:text-secondary-foreground",
+        ghost:
+          "hover:bg-muted hover:text-foreground aria-expanded:bg-muted aria-expanded:text-foreground dark:hover:bg-muted/50",
+        destructive:
+          "bg-destructive/10 text-destructive hover:bg-destructive/20 focus-visible:border-destructive/40 focus-visible:ring-destructive/20 dark:bg-destructive/20 dark:hover:bg-destructive/30 dark:focus-visible:ring-destructive/40",
+        link: "text-primary underline-offset-4 hover:underline",
+      },
+      size: {
+        default:
+          "h-8 gap-1.5 px-2.5 has-data-[icon=inline-end]:pr-2 has-data-[icon=inline-start]:pl-2",
+        xs: "h-6 gap-1 rounded-[min(var(--radius-md),10px)] px-2 text-xs in-data-[slot=button-group]:rounded-lg has-data-[icon=inline-end]:pr-1.5 has-data-[icon=inline-start]:pl-1.5 [&_svg:not([class*='size-'])]:size-3",
+        sm: "h-7 gap-1 rounded-[min(var(--radius-md),12px)] px-2.5 text-[0.8rem] in-data-[slot=button-group]:rounded-lg has-data-[icon=inline-end]:pr-1.5 has-data-[icon=inline-start]:pl-1.5 [&_svg:not([class*='size-'])]:size-3.5",
+        lg: "h-9 gap-1.5 px-2.5 has-data-[icon=inline-end]:pr-2 has-data-[icon=inline-start]:pl-2",
+        icon: "size-8",
+        "icon-xs":
+          "size-6 rounded-[min(var(--radius-md),10px)] in-data-[slot=button-group]:rounded-lg [&_svg:not([class*='size-'])]:size-3",
+        "icon-sm":
+          "size-7 rounded-[min(var(--radius-md),12px)] in-data-[slot=button-group]:rounded-lg",
+        "icon-lg": "size-9",
+      },
+    },
+    defaultVariants: {
+      variant: "default",
+      size: "default",
+    },
+  }
+);
+
+function Button({
+  className,
+  variant = "default",
+  size = "default",
+  ...props
+}: ButtonPrimitive.Props & VariantProps<typeof buttonVariants>) {
+  return (
+    <ButtonPrimitive
+      data-slot="button"
+      className={cn(buttonVariants({ variant, size, className }))}
+      {...props}
+    />
+  );
+}
+
+export { Button, buttonVariants };