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/hover-card.tsx

@@ -0,0 +1,45 @@
+"use client";
+
+import { PreviewCard as PreviewCardPrimitive } from "@base-ui/react/preview-card";
+import { cn } from "cn";
+
+function HoverCard({ ...props }: PreviewCardPrimitive.Root.Props) {
+  return <PreviewCardPrimitive.Root data-slot="hover-card" {...props} />;
+}
+
+function HoverCardTrigger({ ...props }: PreviewCardPrimitive.Trigger.Props) {
+  return <PreviewCardPrimitive.Trigger data-slot="hover-card-trigger" {...props} />;
+}
+
+function HoverCardContent({
+  className,
+  side = "bottom",
+  sideOffset = 4,
+  align = "center",
+  alignOffset = 4,
+  ...props
+}: PreviewCardPrimitive.Popup.Props &
+  Pick<PreviewCardPrimitive.Positioner.Props, "align" | "alignOffset" | "side" | "sideOffset">) {
+  return (
+    <PreviewCardPrimitive.Portal data-slot="hover-card-portal">
+      <PreviewCardPrimitive.Positioner
+        align={align}
+        alignOffset={alignOffset}
+        side={side}
+        sideOffset={sideOffset}
+        className="isolate z-50"
+      >
+        <PreviewCardPrimitive.Popup
+          data-slot="hover-card-content"
+          className={cn(
+            "z-50 w-64 origin-(--transform-origin) rounded-lg bg-popover p-2.5 text-sm text-popover-foreground shadow-md ring-1 ring-foreground/10 outline-hidden duration-100 data-[side=bottom]:slide-in-from-top-2 data-[side=inline-end]:slide-in-from-left-2 data-[side=inline-start]:slide-in-from-right-2 data-[side=left]:slide-in-from-right-2 data-[side=right]:slide-in-from-left-2 data-[side=top]:slide-in-from-bottom-2 data-open:animate-in data-open:fade-in-0 data-open:zoom-in-95 data-closed:aniLine truncated
+            className
+          )}
+          {...props}
+        />
+      </PreviewCardPrimitive.Positioner>
+    </PreviewCardPrimitive.Portal>
+  );
+}
+
+export { HoverCard, HoverCardTrigger, HoverCardContent };