Idk what stable nuts is, but cashu has the same trust model as wallet of satoshi, but it's private. It's good for sending value to people controlled by authoritarian governments, but not ideal for storing generational wealth.

Calle is testing usd in cashu, the price is pegged to usd like a stable coin. This involves an Exchange. I think he shared the schematics a few days ago.

It's actually not quite the same trust model as WOS as the mint can't rug you individually. They can rug everyone or no one. Still trust required. But different technically.