Suceeded to have my Pi 4 displaying at 1920x1080 normally on main display, without real screen on it, without DPI size problem (xrandr commands trick is trash).
Into my config.txt :
#EDID file extracted from my 1920x1080 Samsung S22D300, works :
# Usefull for having something, but 1024x768 only
# Does nothing on Pi4
If someone needs the EDID file :
Should be placed into the fat32 boot partition