fix: bump @playwright/test to 1.62.1 so browser installs stop hanging (#637)

Playwright 1.59.1 cannot install its browsers on macOS/arm64. The failure
is in EXTRACTION, not the download, which is why waiting it out never
worked and why `worktree-setup.sh`'s timeout message ("no progress")
sends readers to the network:

  1.59.1 / chromium-1217  -> stalls at exactly 84 files / 448K, 3 runs
  1.62.1 / chromium-1234  -> completes in ~2 min, 3 runs

In every stalled run the full 173MB zip had already landed in
$TMPDIR/playwright-download-*, and sampling the process showed
oopDownloadBrowserMain.js idle at 0% CPU with every libuv worker parked
in __psynch_cvwait. Same machine, same network, minutes apart.

That hang is what blocks `scripts/worktree-setup.sh`: it kills the
install at its timeout and exits 1, so a fresh worktree never gets
browsers. With this bump the script runs to completion.

Verified against the real stack, not just the install:

  smoke (--project=chromium)  70 passed, 0 failed
  wizard (--project=wizard)   all 14 scenarios passed

Note the suite must be run with MOCK_HA_PORT=8123. e2e/tests/mock-ha.spec.ts
and e2e/tests/health-recovery.spec.ts hardcode http://localhost:8123 while
docker-compose.ci.yml publishes ${MOCK_HA_PORT:-8123} and run-e2e.sh derives
that port from the worktree directory name -- so 7 tests fail in any worktree
whose hash is not 8023. Pre-existing and unrelated to this bump; left alone
here rather than widening the diff.


Claude-Session: https://claude.ai/code/session_016tGBHZEAfKzP9qoJU4NdNY

Co-authored-by: Claude Opus 5 (1M context) <noreply@anthropic.com>

Author: johanzander

e2e/package-lock.json

@@ -12,6 +12,6 @@
   "license": "ISC",
   "type": "commonjs",
   "devDependencies": {
-    "@playwright/test": "^1.59.1"
+    "@playwright/test": "^1.62.1"
   }
 }