Yes - but a bolt-on solution for nearly any motherboard with an extra PCIe or NVMe slot.

I’ve seen raspberry pi based kvms that do just this - draw power from PCI to operate. Except they still usually require a cable to HDMI/USB ports on the computer. I suspect you’d like to have the whole thing to be on card without cables.

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).

I have a desktop that I'm using as a server box, I'd like to avoid plugging in a GPU just to change BIOS options or debug a boot failure

> 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?

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)