feat: add Playwright E2E testing framework

Add @playwright/test, playwright.config.ts, e2e/ smoke test,
and e2e CI job (Chromium-only) that gates build-and-push.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

package.json

@@ -9,7 +9,8 @@
     "lint": "eslint .",
     "preview": "vite preview",
     "test": "NODE_ENV=test vitest run",
-    "test:watch": "NODE_ENV=test vitest"
+    "test:watch": "NODE_ENV=test vitest",
+    "test:e2e": "npx playwright test"
   },
   "dependencies": {
     "@tanstack/react-query": "^5.0.0",
@@ -32,6 +33,7 @@
     "eslint": "^9.39.4",
     "eslint-plugin-react-hooks": "^7.0.1",
     "eslint-plugin-react-refresh": "^0.5.2",
+    "@playwright/test": "^1.49.0",
     "globals": "^17.4.0",
     "jsdom": "^25.0.1",
     "tailwindcss": "^4.0.0",