This library (https://github.com/pubkey/broadcast-channel/blob/master/src/...) from the fantastic RxDB javascript DB library uses WebLocks with a fallback to Broadcast Channel. But, WebLocks are supported on 96% of browsers, so probably safe to just use it exclusively now.
SharedWorker is not very complicated but it's another component to add. It would be cool if this was built into SSE instead.