Any papers you'd recommend?

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