It doesn’t if the screen is connected directly to the frame buffer which can refresh independently. Whether that’s actually implemented this way in hardware, well who knows, but I suspect it is as that’s useful to display any static image. Then just power up the display driver for a microsecond to refresh the image if needed.
I use Session Messenger, on the Oxen network. Love it on principle even tho the implementation is a bit lacking in places.
And there’s Tor… Which is what it is.