Blown capacitor on PS5 affecting display output?

I don’t have a definitive answer, but using some critical thinking I think you can probably get somewhere in the right neighborhood.

It’s definitely a blown component and I would bet money that it’s a capacitor. If I’m looking at the right spot on the board, and I’m guessing I am based on your description, since you said it was under the backplate for the heat sink, this is a capacitor on a processor power line. It looks like it’s on the same line as the other capacitors beneath it, if you follow that sort of wavy trace in the picture from your post. I would wager that the other caps in that same row will be the same value. Obviously this is not a given, but I would consider it a strong possibility.

That being said I would check 2 things with a multimeter. Is this line short to ground or is this line open/broken somewhere? If it’s short to ground, or generally has very little resistance to ground (which may be normal for this line anyways if it is in fact part of CPU, or more likely given your symptoms, GPU power) I would be very confident this is a cap. Evict the ugly cap from the board and see if that resolves the issue. If it’s open, this may not be a cap at all. And then you’re actually going to have to figure out what it is and what the values are.

If it is a cap, you may be able to leave this it off altogether, but given that it’s not your personal device and it’s more than likely part of CPU function, replacing it would certainly be preferable. I would check voltage on the line if possible when the device is running. And measure capacitance on the other components beneath it (If you have a meter that can do that). Best case scenario would be to pull that cap off a donor board and transplant it over (carefully, since the CPU is directly on the other side), but I realize that’s not always possible in the immediate.