I would love for this capability, and also the ability for home assistant to dismiss notifications/alerts which are pending on the thermostat as well.
In my example, I have a vacation home that we must rent out with multiple thermostats. I wish to set HVAC mode to “off” if a certain doors/windows are left open for a period of time, and then turn the system back on (heat/cool) when they are shut. Ideally sending a notification (alert) on the thermostat display itself to inform the user WHY the system has been turned off would be incredibly useful. Also, being able to clear any notification/alert on thermostats would also be useful, so that there are no queued messages on the thermostat(s) when the condition of the notification no longer applies.