Kodi only references the EDID data necessary for audio/video config once at startup, so if the HDMI monitor isn't on/connected before Kodi starts it sees nothing after you turn it on. You can dump the edid data to a local .bin file and then configure xorg.conf to always use the .bin file. This makes the nvidia driver (and Xorg) behave as if it's connected to the monitor, even when it isn't connected. This behaviour has been the same since early OE days so you probably did this once on the OE install and then forgot about it. See Custom EDID [LibreELEC.wiki]
Thanks! Have not touched the OE-pc for at least 5 years, so it could be that I did this during install..