I’ve been working on a very similar sync problem and hit this too. I think the way forward is to use a broadcast channel to elect an individual worker that communicates with all other contexts using the broadcast channel.
It is supported by all browsers. You just have all the tabs try to lock the same resource and have them return a promise in the lock callback. The first one wins and when that tab closes the next one in line gets automatically elected.
The leader can then use a broadcast channel and act as a server for all the other tabs to serialize access to any shared resources.
https://developer.mozilla.org/en-US/docs/Web/API/Web_Locks_A...
It is supported by all browsers. You just have all the tabs try to lock the same resource and have them return a promise in the lock callback. The first one wins and when that tab closes the next one in line gets automatically elected.
The leader can then use a broadcast channel and act as a server for all the other tabs to serialize access to any shared resources.