Add browser-based tests with Playwright and Vitest

Replaces the placeholder test with comprehensive browser tests
covering core, security, and isolation scenarios. Updates CI
workflow and Vite config to run tests in Chromium, Firefox,
and WebKit using @vitest/browser-playwright. Adds the required
dev dependency.

Author: aduros

.github/workflows/ci.yaml

@@ -11,7 +11,7 @@ jobs:
       matrix:
         script:
           - name: Unit tests
-            command: npm test
+            command: npx playwright install --with-deps && npm test
           - name: Typecheck
             command: npm run test:types
           - name: Lint

package-lock.json

@@ -41,6 +41,7 @@
   },
   "devDependencies": {
     "@biomejs/biome": "^2.3.13",
+    "@vitest/browser-playwright": "^4.0.18",
     "lefthook": "^2.0.16",
     "typescript": "^5.9.3",
     "version-bump-prompt": "^6.1.0",