If my memory serves me right, I believe the Greenwise stores are eligible, as the backend of the POS system runs across the same network. Seems to me.
With having such a small footprint of locations and serving as an upscale brand, there will be a limited set of users here that even have knowledge of, let alone, have any experience of shopping there.
I have lived in Florida most of my life and I have never heard of Publix Greenwise. Yes, I am aware of the Greenwise line of products, but I didn't know there was a separate store. All Publix stores carry some amount of Greenwise products. I just thought it was their organic line.