1) Turns off the display in 60 seconds or less. (I think it's more like 10 seconds or less, but I've stopped paying close attention to it, so I am no longer certain about the timing.)
2) Turns the display back on every single time I get a new notification, and turns it back off within a few seconds. Given that this machine is running the Work Messaging Client, that means that the display powers up and down very, very frequently.
So if this is the discoverable "turn off the display" feature that GP was talking about, it's not a fit replacement for the power button on the monitor.
Apple menu -> Lock Screen, and the display will shut off after a few minutes of inactivity on the lock screen or by pressing the Escape key.