Broken out from https://github.com/microsoft/playwright/pull/31900, part of https://github.com/microsoft/playwright/issues/31863. Synchronizes different `useSettings` calls via `useSyncExternalStore`. This saves us from having to drill down settings props everywhere, without the big refactoring that a `Context` would be.
Companion PR of https://github.com/microsoft/playwright-vscode/pull/483