We've been going for 10 years now and have rented with several different companies. They vary on supplies. All have had dish soap, dish washer soap, toilet paper, paper towels, pots and pans,bath towels, etc. The quality and amount varies. I usually bring pump soap for the bathrooms and extra trash bags.
The last several times, we have stayed with Century 21/Cove Mountain. You get 1 roll of toilet paper per bathroom regardless of length of stay. We always bring extra. The pot and pan quality is iffy. The last cabin we stayed in didn't have measuring cups. The pans were so cheap that we burned everything, even grilled cheese. If you are a true cook, bring the basics. A good pot, skillet and sheet pan. In contrast, our friend's cabin had a wonderful kitchen supply. (They were also paying about $500. a night for their cabin).
The quality of supplies vary because many of these cabins are privately owned. Last year we had one that didn't even have a working phone. This irritated me tremendously since our cell phones weren't often connecting in the mountains.