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)

playwright.config.ts

@@ -0,0 +1,26 @@
+import { defineConfig, devices } from "@playwright/test";
+
+export default defineConfig({
+  testDir: "./e2e",
+  fullyParallel: true,
+  forbidOnly: !!process.env.CI,
+  retries: process.env.CI ? 2 : 0,
+  workers: process.env.CI ? 1 : undefined,
+  reporter: "html",
+  use: {
+    baseURL: "http://127.0.0.1:3000",
+    trace: "on-first-retry",
+  },
+  projects: [
+    {
+      name: "chromium",
+      use: { ...devices["Desktop Chrome"] },
+    },
+  ],
+  webServer: {
+    command: "bun run dev",
+    url: "http://127.0.0.1:3000",
+    reuseExistingServer: !process.env.CI,
+    timeout: 120_000,
+  },
+});