Yinrih, especially planetside, may store dishes and cooking utensils in something that washes, dries, and stores the dishes when not in use. The dishes are taken out of storage, used, then put directly back into storage to be washed. This minimizes the need to touch the dishes to move them from a dishwasher to a cabinet.
If they had a separate dishwasher and cabinets, they'd have to wash their paws before moving the dishes from dishwasher to cabinet, and waddle around on their hind feet to transport them so their forepaws don't touch the ground.
In general, cooking employs a lot of the same strategies as surgery, though cooks don't shed their fur the way healers do. In restaurants they may work with glove boxes.
One may be asking why they bother with manual cooking at all if they're a K2 civilization. Canonically, AI hits a hard limit near where it is today on Earth, so fully autonomous robots for complex tasks don't exist. They could use remotely operated robots similar to those seen in telemedicine.