We populate `localStorage` using an init script. Currently, this script
isn't just run for the UI though, but also for all iframes. So we're
resetting `localStorage` every time the UI loads an iframe.
This hasn't been a problem in the past, because the only consumer of
`localStorage`, `Settings`, only read from `localStorage` once and kept
most state in `useState` afterwards. With
https://github.com/microsoft/playwright/pull/31911, this is no longer
true, so the bug starts biting us!
The fix is to ensure the init script isn't run on iframes.
