I have a hard time picturing how an application can be considered anything other than completely broken once a couple threads/workers have deadlocked, so I don't know what any of that quote means. Yeah, I get that browsers isolate tabs and that the damage is contained.
You seem to be expecting these locks to block a thread, but they do not. A "deadlock" with these locks is simply a chunk of heap space holding a bunch of promises that will never resolve, occupying a few slots in the global event loop's select statement.
Also, you don't need to use this API to lock up your web app.