Does it sleep when connected to a different operating system/menu? What cable are you connecting with?
I’ve experienced such a wide variety of behaviour with different hardware, cable and OS combinations that I susect it has more to do with the monitor’s firmware than host computer OS.
Switching to MATE, the display does NOT go to sleep
[UPDATE]
This behaviour only happens when the laptop lid is closed. Keeping the laptop lid open, the monitor goes to sleep... still qualifies as a bug, I think, but it's a workaround.
Other than that, MATE look great, keep on the good work, MATE team
I have the same problem with Ubuntu Mate 20.04 LTS, when my Lenovo laptop is docked into docking the station the external monitor never goes to sleep. It was fine with Ubuntu Mate 18.04 LTS.