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)

lib/http.ts

@@ -0,0 +1,27 @@
+import ky from "ky";
+
+/**
+ * Typed HTTP client built on ky.
+ * Use openapi-fetch alongside this when you have a generated OpenAPI
+ * schema (see openapi-fetch docs: `createClient<paths>({ baseUrl })`).
+ */
+export const apiClient = ky.create({
+  prefix: "/api",
+  timeout: 15_000,
+  retry: {
+    limit: 2,
+    methods: ["get"],
+    statusCodes: [408, 429, 500, 502, 503, 504],
+  },
+});
+
+export const http = {
+  get: <T>(url: string, init?: RequestInit) => apiClient.get(url, init).json<T>(),
+  post: <T>(url: string, body?: unknown, init?: RequestInit) =>
+    apiClient.post(url, { json: body, ...init }).json<T>(),
+  put: <T>(url: string, body?: unknown, init?: RequestInit) =>
+    apiClient.put(url, { json: body, ...init }).json<T>(),
+  patch: <T>(url: string, body?: unknown, init?: RequestInit) =>
+    apiClient.patch(url, { json: body, ...init }).json<T>(),
+  delete: <T>(url: string, init?: RequestInit) => apiClient.delete(url, init).json<T>(),
+};