DPMS does not standby my Samsung monitor

The answer to the question above was to use a HDMI cable supporting DPMS signals.

Note (to avoid the pitfall I fell for): The outer diameter of the cable does not indicate nothing about this. I tried 6 cables in total, the last one did the trick.

DPMS in X11 has three phases (apart from on) which are standby, suspend, and off. You might want to try running

xset dpms force standby

or

xset dpms force suspend

But be aware that it is not always possible to do all of these operations. You can check the Xorg log (might be somewhere in /var/log/Xorg.0.log for the current session, the 0 in there is a screen number and it might be different too) and see what DPMS features are actually supported. On my system when I check for that:

$ grep DPMS /var/log/Xorg.0.log
[    31.954] (II) AMDGPU(0): DPMS capabilities: Off
[    31.970] (==) AMDGPU(0): DPMS enabled
[    31.989] (II) Initializing extension DPMS

I can see that the only state my GPU driver supports is off. That does not mean suspend and standby won't work, but rather that it will actually use the off action instead, even when I do xset dpms force suspend for example.

If, however, you just want the screen to be black, but be usable really fast after a key press or mouse event, then what you might want to look into is simple screen-saver. You must turn off "Quick Power-off in Blank Only Mode" for xscreensaver if you are using that, otherwise it will again just power off your monitor instead.