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>

tools/playwright.sh

@@ -0,0 +1,9 @@
+#!/bin/bash
+set -euo pipefail
+
+# playwright only supports ubuntu/debian officially, and on CI VMs its system deps are pre-installed
+if [ -z "${GITHUB_ACTIONS:-}" ] && [ "$(uname -s)" = "Linux" ] && grep -qE '^ID(_LIKE)?=.*(ubuntu|debian)' /etc/os-release 2>/dev/null; then
+  pnpm exec playwright install --with-deps "$@"
+else
+  pnpm exec playwright install "$@"
+fi