Most progress in data-driven robotics nowadays are done either in unicorn startups or corporate research labs - so you should follow the industry more than academia. The path to good robot performance isn't really in the models themselves - it's highly dependent on how much you can gather high-quality real-life data.

Specifically for laundry folding, Sunday Robotics is probably the state of the art, where they were able to obtain 99.1% success rate and call it "done": https://www.sunday.ai/blog/act-2-preview#solve-standard

If their hero image video and the side by side at (5x) with a human at quote "1x" are "solved" I'm not impressed. I'm faster and more accurate and I am the worst folder in my house (kids included). The human looks like they are doing it slow mo to show children how to.