Add a way to run a job upon reception of a notification
While I'm not sure if this would still fit in the scope of this nice extension, I'd like to propose extending the existing infrastructure to allow scheduling of jobs on LISTEN channels that would run upon reception of an notification raised by an NOTIFY command. That way (and in combination with something like the tcn contrib module) one could design asynchronous triggers or similar constructs.
I don't think it's entirely beyond scope, though if we had the ability to start a job "now" by solving #7, would that address the use-case? For example, your trigger would schedule another command which would be executed asynchronously by pg_cron.
The listen/notify framework is not very suitable for this purpose, particularly since the notifications are a pull-based mechanism rather than a push-based mechanism and it involves parsing sentences.