More importantly, I've seen a few of these proposals mention how important scheduling is, and how executors and tasks need to work together to do that.
AIUI, priority is the way that a task communicates metadata to its executor ("I'm a background task", or "I have something to do with immediate feedback to the user", or by extension, "I'm an audio task" or "I'm a physics simulation task"). It's purpose is to inform the executor's scheduling decisions. It really should scale beyond the immediate needs of UI applications on Apple platforms.
This is why I asked (and continue to wonder) about executors being able to access the TaskLocalStorage of enqueued jobs. If that was possible, you might be able to attach other kinds of priority information which custom executors could use.