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)

vitest.config.ts

@@ -0,0 +1,22 @@
+import { defineConfig } from "vitest/config";
+import path from "node:path";
+
+export default defineConfig({
+  test: {
+    environment: "jsdom",
+    globals: true,
+    setupFiles: ["./vitest.setup.ts"],
+    include: ["**/*.{test,spec}.{ts,tsx}"],
+    exclude: ["node_modules/**", ".next/**", "e2e/**", "playwright/**"],
+    css: false,
+    coverage: {
+      provider: "v8",
+      reporter: ["text", "json", "html"],
+    },
+  },
+  resolve: {
+    alias: {
+      "@": path.resolve(__dirname, "."),
+    },
+  },
+});