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/sheet.tsx

@@ -0,0 +1,125 @@
+"use client";
+
+import * as React from "react";
+import { Dialog as SheetPrimitive } from "@base-ui/react/dialog";
+import { cn } from "cn";
+
+import { Button } from "@/components/ui/button";
+import { XIcon } from "lucide-react";
+
+function Sheet({ ...props }: SheetPrimitive.Root.Props) {
+  return <SheetPrimitive.Root data-slot="sheet" {...props} />;
+}
+
+function SheetTrigger({ ...props }: SheetPrimitive.Trigger.Props) {
+  return <SheetPrimitive.Trigger data-slot="sheet-trigger" {...props} />;
+}
+
+function SheetClose({ ...props }: SheetPrimitive.Close.Props) {
+  return <SheetPrimitive.Close data-slot="sheet-close" {...props} />;
+}
+
+function SheetPortal({ ...props }: SheetPrimitive.Portal.Props) {
+  return <SheetPrimitive.Portal data-slot="sheet-portal" {...props} />;
+}
+
+function SheetOverlay({ className, ...props }: SheetPrimitive.Backdrop.Props) {
+  return (
+    <SheetPrimitive.Backdrop
+      data-slot="sheet-overlay"
+      className={cn(
+        "fixed inset-0 z-50 bg-black/10 transition-opacity duration-150 data-ending-style:opacity-0 data-starting-style:opacity-0 supports-backdrop-filter:backdrop-blur-xs",
+        className
+      )}
+      {...props}
+    />
+  );
+}
+
+function SheetContent({
+  className,
+  children,
+  side = "right",
+  showCloseButton = true,
+  ...props
+}: SheetPrimitive.Popup.Props & {
+  side?: "top" | "right" | "bottom" | "left";
+  showCloseButton?: boolean;
+}) {
+  return (
+    <SheetPortal>
+      <SheetOverlay />
+      <SheetPrimitive.Popup
+        data-slot="sheet-content"
+        data-side={side}
+        className={cn(
+          "fixed z-50 flex flex-col gap-4 bg-popover bg-clip-padding text-sm text-popover-foreground shadow-lg transition duration-200 ease-in-out data-ending-style:opacity-0 data-starting-style:opacity-0 data-[side=bottom]:inset-x-0 data-[side=bottom]:bottom-0 data-[side=bottom]:h-auto data-[side=bottom]:border-t data-[side=bottom]:data-ending-style:translate-y-[2.5rem] data-[side=bottom]:data-starting-style:translate-y-[2.5rem] data-[side=left]:inset-y-0 data-[side=left]:left-0 data-[side=lefLine truncated
+          className
+        )}
+        {...props}
+      >
+        {children}
+        {showCloseButton && (
+          <SheetPrimitive.Close
+            data-slot="sheet-close"
+            render={<Button variant="ghost" className="absolute top-3 right-3" size="icon-sm" />}
+          >
+            <XIcon />
+            <span className="sr-only">Close</span>
+          </SheetPrimitive.Close>
+        )}
+      </SheetPrimitive.Popup>
+    </SheetPortal>
+  );
+}
+
+function SheetHeader({ className, ...props }: React.ComponentProps<"div">) {
+  return (
+    <div
+      data-slot="sheet-header"
+      className={cn("flex flex-col gap-0.5 p-4", className)}
+      {...props}
+    />
+  );
+}
+
+function SheetFooter({ className, ...props }: React.ComponentProps<"div">) {
+  return (
+    <div
+      data-slot="sheet-footer"
+      className={cn("mt-auto flex flex-col gap-2 p-4", className)}
+      {...props}
+    />
+  );
+}
+
+function SheetTitle({ className, ...props }: SheetPrimitive.Title.Props) {
+  return (
+    <SheetPrimitive.Title
+      data-slot="sheet-title"
+      className={cn("font-heading text-base font-medium text-foreground", className)}
+      {...props}
+    />
+  );
+}
+
+function SheetDescription({ className, ...props }: SheetPrimitive.Description.Props) {
+  return (
+    <SheetPrimitive.Description
+      data-slot="sheet-description"
+      className={cn("text-sm text-muted-foreground", className)}
+      {...props}
+    />
+  );
+}
+
+export {
+  Sheet,
+  SheetTrigger,
+  SheetClose,
+  SheetContent,
+  SheetHeader,
+  SheetFooter,
+  SheetTitle,
+  SheetDescription,
+};