test: run frontend unit tests in browsers (#38860)

Run them in headless [vitest browser
mode](https://vitest.dev/guide/browser/) in chromium and firefox.
Similar UX than current tests, it's about 5 times as slow (goes from 1s
to 5s on my machine), but definitely worth it as it removes all
happy-dom problems.

---------

Signed-off-by: silverwind <me@silverwind.io>

package.json

@@ -83,6 +83,7 @@
     "@types/toastify-js": "1.12.4",
     "@typescript-eslint/parser": "8.67.0",
     "@vitejs/plugin-vue": "6.0.8",
+    "@vitest/browser-playwright": "4.1.10",
     "@vitest/eslint-plugin": "1.6.27",
     "eslint": "10.8.1",
     "eslint-import-resolver-typescript": "4.4.5",
@@ -94,7 +95,6 @@
     "eslint-plugin-vue-scoped-css": "3.1.3",
     "eslint-plugin-wc": "3.1.0",
     "globals": "17.11.0",
-    "happy-dom": "20.11.2",
     "jiti": "2.7.0",
     "linguist-languages": "9.4.0",
     "markdownlint-cli": "0.49.1",