As a result, we were looking into a very similar system where we each have an LED signboard, speaker, and priority lights on the top of a small device that lives on top of our monitors along with an app where she can select "not urgent, but you should know", "when you have a moment", "as soon as you can", and "urgent, right now" in an app, with an optional message, and the device makes a tone and lights the lights associated with the most recent, highest priority message as well as reminding every five minutes.
I'm playing with an ESP32 right now to implement, but it's nice to see that the entire concept isn't entirely unprecidented.