Something like Intel AMT? Some prosumer motherboards like ASRock Rack have out of band management controllers in them.
Example: https://geekworm.com/collections/pikvm (but I think this still requires separate power)
To do this, wouldn’t you effectively need to make a graphics card (VGA would work) where a separate chip could read the screen buffer? And somehow get this card to display preferentially over the on-board video card?
I’m sure the all in one card version exists, but honestly a cabled version seems more robust (w/o vendor support that is).
If you do basic VGA (and UEFI), that'd be plenty for most. If it had a local output it'd be great for systems without video on the cpu (am4 non-apus, but also others)