Everything I see indicates a focus issue. Especially with the cuts all looking the same after you manually changed the focal height for each operation. If that was done correctly, it should have changed the focus point for each job and the cut lines would look different.
The camera focus is fixed from the factory and won’t inhibit the cutting ability. I don’t know why some of them are that fuzzy. You’d only have to be close with that wide of a lens for everything to stay in focus. That said, the lens doesn’t need perfect focus generally to read the QR codes.
All in all, I think the reality here is that you’ll need to get a proper crumbtray in, and then cut the gift of good measure to see what it looks like. (To get actual Glowforge support - it needs to be Proofgrade material on a proper crumbtray, with a known good file from GF - to eliminate other variables).
Presumably one of those pins in the ribbon cable connecting the head also controls the AF motor, so it might be worth checking to make sure the ribbon connector is seated correctly. If so, disconnect it, take a picture of the pins and post it up here.