If you want the most precise color reproduction from a computer monitor, you calibrate it. But calibration mostly changes the PC, not the monitor, apart from the selection of basic color profile and brightness/contrast.
Is there any standard how to set up a monitor connected directly to the HDMI output of a DSLR or DSLM, used as a viewfinder or review device - or is it "just set the color profile to sRGB, turn off all "picture enhancement" options and pray hard"?
Assumption: Camera is set up to use sRGB.