Would that really need AI though? I guess recognizing the particular item and then deciding how to fold/hang it would be some sort of ML. Again though, that's just a bunch of if statements being labeled as AI.
There are lots of laundry-folding "graduate student robotics project" systems. Most of the videos of them are sped up 8x to make them "merely slow", and involve a rough surface to drag the material against - since they typically use one gripper; two-coordinated-grippers is still a mostly demo/research thing.
If it takes 3 days to fold a load of washing, it's still quicker than it takes me now. For commercial use it wouldn't work, but for consumers speed is not an issue.
Mine tends to go from the drier to laying out flat on top of the drier. So the fact it gets folded would be great. Every now and then I actually fold and put away and I feel like an adult. We try not to do that much around here