I’ve connected Cintiqs, portable monitors and regular monitors to my laptop. I’ve never seen a DP or MDP or HDMI screen that didn’t also have another power source, but maybe they exist. In any case those didn’t seem to affect my battery much, because they were plugged.
I have a portable monitor that connects via usb-c, that one drains the battery but I usually use it with my laptop plugged so I can’t really tell what kind of impact it has.